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  • Homeomorphism
    ...{{M|(Y,d')}} they are said to be ''homeomorphic''<ref name="FA">Functional Analysis - George Bachman Lawrence Narici</ref> if:
    5 KB (731 words) - 22:58, 22 February 2017
  • Injection
    ...th> are mapped to the same thing in <math>Y</math>. That is<ref name="API">Analysis: Part 1 - Elements - Krzysztof Maurin</ref>: ...rt 1 - Elements - Krzysztof Maurin</ref><ref name="RAAA">Real and Abstract Analysis - Edwin Hewitt and Karl Stromberg</ref>
    3 KB (463 words) - 21:50, 8 May 2018
  • Open set
    {{Definition|Metric Space|Topology|Functional Analysis}}
    4 KB (677 words) - 02:26, 29 November 2015
  • Open ball
    {{Definition|Metric Space|Topology|Functional Analysis}}
    4 KB (842 words) - 02:00, 29 November 2015
  • Metric space
    * <math>d:X\times X\rightarrow\mathbb{R}_+</math><ref name="Analysis">Analysis - Part 1: Elements - Krzysztof Maurin</ref>, Note that here I prefer the no
    2 KB (336 words) - 06:07, 27 November 2015
  • Nabla
    I've seen a book (Vector Analysis and Cartesian Tensors - Third Edition - D E Borune & P C Kendall - which is
    1 KB (245 words) - 18:35, 13 February 2015
  • Continuous map
    ...{M|f:X\rightarrow Y}} is continuous if<ref name="KMAPI">Krzysztof Maurin - Analysis - Part 1: Elements</ref>: {{Todo|This - See Analysis I - Maurin page 44 if stuck}}
    6 KB (972 words) - 01:44, 14 October 2016
  • Connected (topology)
    ...is no such separation then the space is ''connected''<ref name="Analysis">Analysis - Part 1: Elements - Krzysztof Maurin</ref>
    5 KB (866 words) - 01:52, 1 October 2016
  • Closed set
    ...logy - Third Edition - Mendelson</ref><ref name="KMAPI">Krzyzstof Maurin - Analysis - Part I: Elements</ref>.
    1 KB (238 words) - 15:36, 24 November 2015
  • Closure, interior and boundary
    ...e closure can be defined as:<ref>Walter Rudin - Principals of Mathematical Analysis</ref>
    1 KB (210 words) - 00:20, 9 March 2015
  • Triangle inequality
    {{Theorem Of|Real Analysis}}
    3 KB (546 words) - 13:05, 19 February 2016
  • Function
    A function is a special kind [[relation]]<ref name="API">Analysis - Part 1: Elements - Krzysztof Maurin</ref>, for a relation:
    4 KB (659 words) - 13:01, 19 February 2016
  • Relation
    ...symmetric|Type_identitive}}Antisymmetric<ref name="RAAA">Real and Abstract Analysis - Edwin Hewitt and Karl Stromberg</ref><br/>({{AKA}} Identitive<ref name="A
    4 KB (762 words) - 20:07, 20 April 2016
  • Norm
    ...uding the brilliant [[Books:Analysis - Part 1: Elements - Krzysztof Maurin|Analysis - Part 1: Elements - Krzysztof Maurin]] referenced here state ''explicitly' ...for more information, this relationship is very important in [[Functional analysis]])
    6 KB (1,026 words) - 20:33, 9 April 2017
  • Absolute value
    {{Definition|Real Analysis}}
    795 B (110 words) - 18:15, 18 March 2016
  • Cauchy-Schwarz inequality
    {{Theorem Of|Real Analysis}}
    3 KB (609 words) - 13:04, 4 April 2017
  • Index of notation
    * Functional Analysis * Real Analysis
    9 KB (1,490 words) - 06:13, 1 January 2017
  • Sequence
    ...et Theory, third edition, Jech and Hrbacek</ref><ref name="Analysis">p11 - Analysis - Part 1: Elements - Krzysztof Maurin</ref>, <math>f:\mathbb{N}\rightarrow {{Definition|Set Theory|Real Analysis|Functional Analysis}}
    2 KB (419 words) - 18:12, 13 March 2016
  • Sequential compactness
    ====Functional Analysis====
    1 KB (228 words) - 15:37, 24 November 2015
  • Cauchy criterion for convergence
    {{Definition|Real Analysis|Functional Analysis}} {{Theorem Of|Real Analysis|Functional Analysis}}
    898 B (145 words) - 15:26, 24 November 2015
  • Convergence of a sequence
    {{Definition|Real Analysis|Topology|Functional Analysis|Metric Space}}
    794 B (122 words) - 13:30, 5 December 2015
  • Vector dot product
    {{Definition|Vector Analysis|Linear Algebra}}
    534 B (96 words) - 02:04, 29 March 2015
  • Equivalence class
    ...again {{M|a}} is the representative of the class.<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref>
    1 KB (160 words) - 20:00, 14 November 2015
  • Motivation for tangent space definitions
    This becomes clear with the dimensional analysis of the transition (stated again here)
    4 KB (790 words) - 22:25, 12 April 2015
  • Inner product
    ...- Lecture Notes - Richard Sharp - Sep 2014</ref><ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref> is a map: {{Definition|Linear Algebra|Functional Analysis}}
    6 KB (1,016 words) - 12:57, 19 February 2016
  • Hilbert space
    A ''Hilbert space''<ref>Functional Analysis I - Lecture Notes - Richard Sharp - Sep 2014</ref> is a {{Vector space|H}} {{Definition|Functional Analysis}}
    573 B (93 words) - 17:34, 21 April 2015
  • Limit
    {{Definition|Real Analysis}}
    2 KB (310 words) - 18:23, 8 January 2016
  • Index of norms and absolute values
    * Functional Analysis * Real Analysis
    1 KB (207 words) - 09:16, 9 June 2015
  • Krzysztof Maurin's notation
    ==Analysis - Part I: Elements== ! Read as<ref name="part1">Analysis - Part I: Elements - Krzysztof Maurin</ref>
    1 KB (173 words) - 14:51, 18 June 2015
  • Partition (abstract algebra)
    Then the ''family'' {{M|\{A_i\}_{i\in I} }} is called<ref name="Analysis">Analysis - Part 1: Elements - Krzystof Maurin</ref> ''the partition of the set {{M|B
    2 KB (316 words) - 16:03, 18 June 2015
  • Notes:Compactness and sequences
    Analysis: Part 1 - Elements by Krzysztof Maurin has a great bit on compactness! It u
    336 B (58 words) - 03:59, 22 June 2015
  • Bounded set
    {{Definition|Metric Space|Functional Analysis|Analysis}}
    2 KB (409 words) - 23:31, 29 October 2016
  • Isometry
    ...Y,d')}}<br/> we have {{M|1=d(x,y)=d'(f(x),f(y))}}<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref>
    1 KB (212 words) - 13:13, 9 July 2015
  • Cauchy sequence
    {{Definition|Functional Analysis|Metric Space|Real Analysis|Topology}}
    669 B (81 words) - 21:10, 20 April 2016
  • Complete metric space
    ...ional Analysis - George Bachman and Lawrence Narici</ref><ref name="KMAPI">Analysis - Part I: Elements - Krzysztof Maurin</ref>. That is to say:
    2 KB (382 words) - 15:36, 24 November 2015
  • Inner product examples
    ** Use contrapositive to do this, and a bit of analysis [[Category:Functional Analysis]]
    3 KB (678 words) - 16:16, 11 July 2015
  • Inner product space
    ...r a ''pre-[[Hilbert space|hilbert]] space'') is a<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref>: {{Definition|Functional Analysis}}
    949 B (161 words) - 21:08, 11 July 2015
  • Normed space
    ...al Analysis - George Bachman and Lawrence Narici</ref><ref name="Analysis">Analysis - Part 1: Elements - Krzysztof Maurin</ref>: {{Definition|Functional Analysis|Linear Algebra}}
    813 B (129 words) - 22:13, 11 July 2015
  • Euclidean n-space
    There are two forms of ''Euclidean {{n|space}}''<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref>, we have: {{Definition|Functional Analysis|Real Analysis|Complex Analysis}}
    2 KB (398 words) - 14:17, 12 July 2015
  • Inequalities for inner products
    ! [[Cauchy-Schwarz inequality]]<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref> [[Category:Functional Analysis]]
    1 KB (214 words) - 14:52, 12 July 2015
  • Perpendicular
    ...we define {{M|x}} and {{M|y}} being perpendicular<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref> if: {{Definition|Functional Analysis}}
    346 B (54 words) - 14:56, 12 July 2015
  • Index of spaces
    * Analysis * Functional analysis
    3 KB (612 words) - 21:06, 29 February 2016
  • Space of square-summable sequences
    ...ce|sequences]] of either complex, or real numbers<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref>. That is: {{Definition|Functional Analysis}}
    893 B (141 words) - 15:47, 12 July 2015
  • Orthonormal set
    ...space|i.p.s]], we say {{M|S}} is ''orthonormal''<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref> if: {{Definition|Functional Analysis}}
    1 KB (154 words) - 16:12, 12 July 2015
  • Discrete metric and topology/Metric space definition
    ...t. The ''discrete''{{rITTGG}} metric, or ''trivial metric''<ref>Functional Analysis - George Bachman and Lawrence Narici</ref> is the [[Metric space|metric]] d
    1,004 B (160 words) - 06:08, 27 November 2015
  • Min/max
    {{Definition|Set Theory|Real Analysis|Measure Theory}}
    884 B (144 words) - 02:51, 3 August 2015
  • Positive and negative parts of a function
    {{Definition|Real Analysis|Measure Theory|Set Theory}}
    518 B (84 words) - 01:21, 5 August 2015
  • Limit of increasing sequence of sets
    {{Definition|Set Theory|Measure Theory|Real Analysis}}
    2 KB (334 words) - 17:52, 21 August 2015
  • Classes of continuously differentiable functions
    {{Definition|Real Analysis|Manifolds|Differential Geometry|Measure Theory}}
    3 KB (632 words) - 20:32, 16 October 2015
  • Real-valued function
    {{Definition|Measure Theory|Manifolds|Differential Geometry|Functional Analysis}}
    807 B (117 words) - 23:15, 21 October 2015
  • Algebra
    {{Definition|Measure Theory|Manifolds|Differential Geometry|Real Analysis|Linear Algebra}}
    579 B (80 words) - 15:39, 27 March 2016
  • Class of smooth real-valued functions on R-n
    {{Definition|Manifolds|Functional Analysis|Real Analysis|Measure Theory}}
    2 KB (259 words) - 23:41, 21 October 2015
  • Class of smooth real-valued functions on R-n/Structure
    {{Definition|Manifolds|Differential Geometry|Real Analysis|Measure Theory}}
    636 B (103 words) - 23:43, 21 October 2015
  • Algebra (disambiguation)
    {{Definition|Measure Theory|Manifolds|Differential Geometry|Real Analysis|Linear Algebra}}
    579 B (80 words) - 05:27, 1 January 2017
  • Differentiability
    ...(a+t)-f(a)}{t}\right)}}, provided this [[limit]] exists<ref name="Munkres">Analysis on Manifolds - James R. Munkres</ref>. This is the same as: {{Definition|Real Analysis|Manifolds}}
    1 KB (231 words) - 18:47, 19 November 2015
  • Neighbourhood
    ...}} is a ''neighbourhood'' of {{M|x}} if<ref name="KMAPI">Krysztof Maurin - Analysis - Part 1: Elements</ref><ref name="BMITT">Introduction to topology - Third
    3 KB (449 words) - 20:23, 28 October 2016
  • Limit (sequence)
    ...the sequence {{M|1=(x_n)}} is said to<ref name="KMAPI">Krzysztof Maurin - Analysis - Part 1: Elements</ref><ref group="Note">Actually Maurin gives: {{Definition|Real Analysis|Metric Space|Topology}}
    5 KB (890 words) - 13:56, 5 December 2015
  • Cauchy sequence/Definition
    {{Definition|Real Analysis|Functional Analysis|Topology|Metric Space}}
    1,000 B (180 words) - 13:55, 5 December 2015
  • Cauchy sequence/Short definition
    ...\subseteq X}} is said to be a ''Cauchy sequence''<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref>{{rAPIKM}} if: {{Definition|Real Analysis|Functional Analysis|Topology|Metric Space}}
    519 B (82 words) - 13:55, 5 December 2015
  • Every sequence in a compact space is a lingering sequence
    {{Theorem Of|Metric Space|Real Analysis|Functional Analysis}}
    863 B (128 words) - 16:20, 6 December 2015
  • Completeness
    {{Definition|Real Analysis|Topology|Metric Space}}
    86 B (10 words) - 15:27, 24 November 2015
  • Subsequence
    {{Definition|Real Analysis|Set Theory|Functional Analysis}}
    2 KB (356 words) - 23:27, 16 November 2016
  • Topological space/Definition
    {{Definition|Topology|Metric Space|Functional Analysis}}
    1 KB (227 words) - 18:09, 20 April 2016
  • Interior point (topology)
    {{Definition|Metric Space|Functional Analysis|Topology}}
    3 KB (492 words) - 09:48, 30 December 2016
  • Interior
    {{Definition|Metric Space|Topology|Functional Analysis}}
    2 KB (263 words) - 19:28, 16 February 2017
  • Open balls
    {{Definition|Metric Space|Real Analysis|Topology}}
    229 B (36 words) - 10:56, 1 December 2015
  • Totally bounded
    {{Definition|Metric Space|Topology|Real Analysis}}
    626 B (101 words) - 19:44, 27 May 2016
  • Sub-sequence
    {{Definition|Set Theory|Real Analysis|Functional Analysis}}
    104 B (11 words) - 15:14, 1 December 2015
  • Subsequence/Definition
    {{Definition|Set Theory|Real Analysis|Functional Analysis}}
    3 KB (484 words) - 21:54, 16 November 2016
  • Convergence (sequence)
    {{Definition|Metric Space|Topology|Functional Analysis}}
    157 B (22 words) - 16:13, 1 December 2015
  • Convergent (sequence)
    {{Definition|Functional Analysis|Real Analysis|Metric Space}}
    204 B (28 words) - 16:16, 1 December 2015
  • Every lingering sequence has a convergent subsequence
    {{Theorem Of|Functional Analysis|Real Analysis|Metric Space|Topology}}
    448 B (50 words) - 17:16, 6 December 2015
  • If a subsequence of a Cauchy sequence converges then the Cauchy sequence itself also converges
    {{Theorem Of|Metric Space|Real Analysis|Topology|Functional Analysis}}
    2 KB (357 words) - 11:31, 27 May 2016
  • Lingering sequence
    {{Definition|Real Analysis|Functional Analysis|Metric Space|Topology}}
    1 KB (155 words) - 16:48, 6 December 2015
  • Norm/Heading
    ...e [[topology theorems]] apply. Norms are especially useful in [[functional analysis]] and also for [[differentiation]].
    1 KB (194 words) - 19:28, 25 January 2016
  • Differentiation
    {{Definition|Manifolds|Topology|Metric Space|Functional Analysis}}
    98 B (9 words) - 11:55, 8 January 2016
  • Derivative
    * [[Derivative (analysis)]] - the derivative of a [[mapping]] between two [[normed]] spaces (this is {{Definition|Analysis|Measure Theory}}
    291 B (37 words) - 10:30, 11 March 2016
  • Fréchet derivative
    {{Definition|Differentiation|Analysis|Real Analysis|Functional Analysis}}
    105 B (10 words) - 10:47, 11 March 2016
  • Gateaux derivative
    {{Definition|Differentiation|Analysis|Real Analysis|Functional Analysis}}
    110 B (10 words) - 10:44, 11 March 2016
  • Weak derivative
    {{Definition|Differentiation|Analysis|Real Analysis|Functional Analysis}}
    110 B (10 words) - 10:45, 11 March 2016
  • Strong derivative
    ...or and add "total derivative" to list of AKA names, see also [[derivative (analysis)]] and do the same thing there}} {{Definition|Differentiation|Analysis|Functional Analysis|Real Analysis}}
    1 KB (212 words) - 11:55, 11 March 2016
  • Site:Mathematical subject index/Index
    * [[Analysis (subject)|Analysis]] ** [[Complex Analysis (subject)|Complex Analysis]]
    2 KB (265 words) - 14:53, 26 February 2016
  • Poset
    ...ires references|I know Introduction to Category Theory has the definition, Analysis (Maurin) might too!}}
    421 B (60 words) - 21:24, 19 April 2016
  • Order Theory (subject)
    Some order theory is desired for parts of [[Analysis (subject)|analysis]], for this I recommend the reader know at least about [[partial ordering|p
    2 KB (217 words) - 15:26, 26 February 2016
  • Linear Algebra (subject)
    ...onwards via the [[tensor product]]. This has links to [[Analysis (subject)|analysis]] via [[Differentiation (subject)|differentiation]] as a vector space equip
    1 KB (150 words) - 15:09, 26 February 2016
  • Differentiation (subject)
    [[Category:Real Analysis]] [[Category:Analysis]]
    691 B (94 words) - 14:56, 26 February 2016
  • Continuity
    {{Definition|Topology|Metric Space|Real Analysis}}
    80 B (9 words) - 16:05, 26 February 2016
  • Bounded
    {{Definition|Topology|Linear Algebra|Functional Analysis|Metric Space}}
    506 B (80 words) - 19:44, 27 May 2016
  • Bounded (linear map)
    {{Definition|Linear Algebra|Functional Analysis|Topology|Metric Space}}
    105 B (12 words) - 18:06, 26 February 2016
  • Bounded (sequence)
    {{Definition|Analysis|Functional Analysis|Metric Space|Topology}}
    97 B (10 words) - 16:38, 26 February 2016
  • Bounded linear map
    {{Definition|Linear Algebra|Functional Analysis|Topology|Metric Space}}
    618 B (104 words) - 21:30, 19 April 2016
  • Equivalent conditions for a linear map between two normed spaces to be continuous everywhere
    {{Theorem Of|Linear Algebra|Functional Analysis|Metric Space}}
    3 KB (491 words) - 01:35, 28 February 2016
  • Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/1 implies 2
    {{Theorem Of|Linear Algebra|Functional Analysis}}
    5 KB (1,064 words) - 02:24, 28 February 2016
  • Null sequence
    {{Definition|Functional Analysis|Analysis|Metric Space|Topology}}
    744 B (118 words) - 21:28, 19 April 2016
  • Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/2 implies 3
    {{Theorem Of|Linear Algebra|Functional Analysis}}
    6 KB (1,091 words) - 00:37, 28 February 2016
  • Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/3 implies 4
    {{Theorem Of|Linear Algebra|Functional Analysis}}
    3 KB (611 words) - 01:17, 28 February 2016
  • Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/4 implies 1
    {{Theorem Of|Linear Algebra|Functional Analysis}}
    2 KB (279 words) - 01:34, 28 February 2016
  • Equivalence of Cauchy sequences/Definition
    {{Definition|Analysis|Functional Analysis|Topology|Metric Space}}
    635 B (92 words) - 20:12, 29 February 2016
  • Equivalence of Cauchy sequences/Proof
    {{Theorem Of|Metric Space|Topology|Functional Analysis|Analysis}}
    7 KB (1,404 words) - 21:02, 20 April 2016
  • Equivalence of Cauchy sequences
    {{Definition|Metric Space|Topology|Functional Analysis|Analysis|Real Analysis}}
    1 KB (153 words) - 21:05, 20 April 2016
  • Derivative (analysis)
    {{Definition|Differentiation|Linear Algebra|Analysis}}
    3 KB (497 words) - 10:46, 11 March 2016
  • Integral
    * [[Integral (real analysis)]] * [[Integral (complex analysis)]]
    454 B (55 words) - 13:05, 12 March 2016
  • Bounded sequence
    {{Definition|Topology|Metric Space|Analysis|Real Analysis|Functional Analysis}}
    1 KB (268 words) - 08:31, 13 March 2016
  • Reverse triangle inequality
    {{Theorem Of|Functional Analysis}}
    2 KB (306 words) - 09:28, 13 March 2016
  • Every convergent sequence is Cauchy
    {{Theorem Of|Metric Space|Functional Analysis|Topology|Real Analysis}}
    779 B (135 words) - 21:23, 19 April 2016
  • Notes:Measures
    # [[Books:Real and Abstract Analysis - Edwin Hewitt & Karl Stromberg]] ...2: Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis - Krzysztof Maurin]]
    5 KB (771 words) - 03:06, 21 March 2016
  • Algebra (linear algebra)
    {{Definition|Manifolds|Differential Geometry|Functional Analysis}}
    2 KB (351 words) - 05:26, 1 January 2017
  • Monotonic
    {{Definition|Set Theory|Order Theory|Measure Theory|Real Analysis}}
    1 KB (190 words) - 04:50, 9 April 2016
  • Greater than or equal to
    {{Definition|Real Analysis|Elementary Set Theory|Order Theory}}
    1 KB (152 words) - 15:56, 9 April 2016
  • Greater than or equal to/Epsilon form
    {{Theorem Of|Order Theory|Elementary Set Theory|Real Analysis}}
    1 KB (249 words) - 15:07, 9 April 2016
  • Infimum
    {{Definition|Order Theory|Real Analysis|Set Theory}} {{Definition|Order Theory|Real Analysis|Set Theory}}
    5 KB (851 words) - 08:55, 29 July 2016
  • Metric induced by a norm
    {{Definition|Metric Space|Topology|Functional Analysis}}
    100 B (13 words) - 11:36, 11 May 2016
  • Kronecker delta
    {{Definition|Linear Algebra|Real Analysis|Analysis|Smooth Manifolds|Manifolds}}[[Category:Convenience symbols]]
    716 B (112 words) - 12:24, 14 May 2016
  • Notes:Measures - Real and Abstract Analysis - Hewitt & Stromberg
    ...sures]] series, covering the terminology used in [[Books:Real and Abstract Analysis - Edwin Hewitt & Karl Stromberg]].
    452 B (71 words) - 18:04, 31 May 2016
  • Real numbers
    {{Definition|Real Analysis|Functional Analysis|Set Theory|Analysis|Topology}}
    108 B (13 words) - 21:35, 26 February 2017
  • Cantor's construction of the real numbers/Definition
    {{Definition|Real Analysis}}
    899 B (134 words) - 11:47, 2 June 2016
  • Cantor's construction of the real numbers
    {{Definition|Real Analysis}}
    331 B (41 words) - 11:48, 2 June 2016
  • The real numbers
    {{Definition|Real Analysis}}
    1 KB (200 words) - 21:31, 26 February 2017
  • Axiom of completeness/Statement
    {{Theorem Of|Real Analysis}}
    304 B (43 words) - 13:57, 2 June 2016
  • Axiom of completeness
    {{Theorem Of|Real Analysis}}
    467 B (69 words) - 13:06, 30 July 2016
  • Mean value theorem
    {{Stub page|grade=A*|msg=A fundamental page of analysis, demote to grade C once the content is fleshed out and referenced properly. {{Theorem Of|Real Analysis|Smooth Manifolds}}
    931 B (144 words) - 06:48, 4 June 2016
  • Notes:Mean value theorem
    {{Notes|Smooth Manifolds|Real Analysis}}
    3 KB (529 words) - 08:07, 4 June 2016
  • Notes:Diff algorithm
    ==Diffgraph algorithm analysis===
    12 KB (2,041 words) - 00:50, 27 June 2016
  • Linear combination
    {{Functional analysis navbox}} {{Definition|Linear Algebra|Functional Analysis}}
    1 KB (200 words) - 07:37, 29 July 2016
  • Epsilon form of inequalities
    {{Theorem Of|Real Analysis|Analysis}}
    528 B (92 words) - 17:03, 17 August 2016
  • Dense
    ...onal Analysis - Volume 1: A gentle introduction - Dzung Minh Ha|Functional Analysis - V1 - Dzung M. Ha]] - can't use references in reference tag!)</ref> {{Definition|Topology|Metric Space|Functional Analysis}}
    6 KB (1,097 words) - 04:15, 1 January 2017
  • Metric induced by the norm
    {{Definition|Functional Analysis|Metric Space}}
    86 B (11 words) - 20:00, 10 October 2016
  • Dense set
    {{Definition|Topology|Metric Space|Functional Analysis}}
    76 B (8 words) - 19:57, 28 October 2016
  • Topological space induced by the metric space
    {{Definition|Topology|Metric Space|Functional Analysis}}
    114 B (14 words) - 20:01, 28 October 2016
  • Inner-product space
    {{Definition|Analysis|Functional Analysis|Metric Space|Topology}}
    99 B (11 words) - 23:07, 29 October 2016
  • Functional Analysis (subject)
    ...he familiar structure of say {{M|\mathbb{R} }} then functional analysis is analysis from a generic [[metric space]] instead (or [[normed space]] or [[inner-pro
    302 B (45 words) - 23:08, 29 October 2016
  • Unbounded
    {{Definition|Functional Analysis|Analysis|Topology|Metric Space}}
    101 B (11 words) - 23:24, 29 October 2016
  • Equivalent conditions to a set being bounded/Statement
    {{Theorem Of|Metric Space|Functional Analysis|Analysis|Topology}}
    720 B (124 words) - 23:41, 29 October 2016
  • Equivalent conditions to a set being bounded/1 implies 2
    ...C|easy=true|msg=Easy and routine proof. If stuck see page 13 in Functional Analysis, Dzung Minh Ha}}
    123 B (21 words) - 23:45, 29 October 2016
  • Equivalent conditions to a set being bounded/2 implies 1
    ...C|easy=true|msg=Easy and routine proof. If stuck see page 13 in Functional Analysis, Dzung Minh Ha}}
    123 B (21 words) - 23:45, 29 October 2016
  • Equivalent conditions to a set being bounded
    {{Theorem Of|Analysis|Functional Analysis|Topology|Metric Space}}
    1 KB (167 words) - 23:12, 18 March 2017
  • Set of continuous functions
    {{Definition|Metric Space|Topology|Functional Analysis|Analysis}}
    138 B (16 words) - 03:30, 3 November 2016
  • C(I,X)
    {{Definition|Topology|Functional Analysis|Analysis}}
    1 KB (258 words) - 05:08, 3 November 2016
  • Omega(X,b)
    {{Definition|Algebraic Topology|Homotopy Theory|Topology|Functional Analysis}}
    2 KB (364 words) - 04:47, 3 November 2016
  • The set of continuous functions between topological spaces
    {{Definition|Functional Analysis|Analysis|Topology|Metric Space}}
    1 KB (235 words) - 05:02, 3 November 2016
  • IT-Ebooks.info & obtaining pdfs of books
    ...g on a lengthy train journey). Is this bad or good? I want to provide some analysis of the subject.
    3 KB (637 words) - 11:10, 7 November 2016
  • Normed spaces
    {{Definition|Topology|Functional Analysis|Metric Space|Analysis}}
    92 B (10 words) - 10:00, 11 November 2016
  • Total derivative
    {{Definition|Differentiation|Analysis}}
    2 KB (313 words) - 01:27, 15 November 2016
  • Convergent sequence
    {{Definition|Analysis|Functional Analysis|Real Analysis|Metric Space|Topology}}
    110 B (12 words) - 23:53, 17 November 2016
  • Series (summation)
    {{Stub page|grade=A|msg=Created for functional analysis - work needed}} {{Definition|Functional Analysis|Analysis|Real Analysis|Metric Space|Topology}}
    1 KB (191 words) - 20:13, 18 November 2016
  • Absolute value (object)
    {{Definition|Abstract Algebra|Functional Analysis|Ring Theory|Real Analysis}}
    2 KB (350 words) - 05:25, 21 November 2016
  • Converges (sequence)
    {{Definition|Real Analysis|Analysis|Topology|Metric Space}}
    90 B (10 words) - 09:41, 22 November 2016
  • UTLOC:1
    {{Theorem Of|Metric Space|Analysis|Real Analysis|Functional Analysis}}
    4 KB (795 words) - 10:03, 22 November 2016
  • If a real series converges then its terms tend to zero
    {{Theorem Of|Functional Analysis|Real Analysis|Analysis}}
    1 KB (233 words) - 10:09, 22 November 2016
  • Real sequences
    {{Definition|Functional Analysis|Analysis|Metric Space|Real Analysis}}
    98 B (11 words) - 05:42, 23 November 2016
  • Real sequence
    {{Definition|Analysis|Functional Analysis|Real Analysis}}
    683 B (115 words) - 05:44, 23 November 2016
  • Operations on convergent sequences of real numbers
    {{Theorem Of|Real Analysis|Analysis|Functional Analysis|Metric Space}}
    5 KB (900 words) - 05:45, 23 November 2016
  • The vector space of all linear maps between two spaces
    {{Definition|Linear Algebra|Functional Analysis}} {{Theorem Of|Linear Algebra|Functional Analysis}}
    2 KB (400 words) - 21:16, 17 November 2016
  • Set of all linear maps between spaces
    {{Definition|Linear Algebra|Functional Analysis}}
    118 B (16 words) - 21:16, 17 November 2016
  • The space of all linear maps between spaces
    {{Definition|Linear Algebra|Functional Analysis}}
    118 B (16 words) - 21:17, 17 November 2016
  • Comparison test for real series/Statement
    {{Theorem Of|Functional Analysis|Analysis|Metric Space|Real Analysis}}
    797 B (144 words) - 06:16, 23 November 2016
  • A monotonically increasing sequence bounded above converges
    {{Theorem Of|Real Analysis|Analysis|Functional Analysis|Metric Space}}
    3 KB (493 words) - 07:21, 23 November 2016
  • Comparison test for real series
    ...e|grade=A*|msg=Flesh out, link, then demote. This is needed for functional analysis}} {{Theorem Of|Real Analysis|Analysis|Metric Space|Functional Analysis}}
    766 B (105 words) - 07:28, 23 November 2016
  • Bernstein polynomial/Definition
    {{Definition|Analysis|Real Analysis|Functional Analysis}}
    447 B (69 words) - 10:44, 25 November 2016
  • Bernstein polynomial
    {{XXX|More analysis required}} {{Definition|Real Analysis|Analysis|Functional Analysis}}
    547 B (91 words) - 10:44, 25 November 2016
  • Weierstrass approximation theorem
    {{Theorem Of|Analysis|Real Analysis|Functional Analysis}}
    8 KB (1,610 words) - 08:17, 28 December 2016
  • A function is continuous if and only if the pre-image of every basis element is open
    {{Stub page|grade=B|msg=Important for functional analysis.<br/> {{Theorem Of|Topology|Metric Space|Functional Analysis}}
    4 KB (839 words) - 18:35, 17 December 2016
  • Index of notation/L
    ! rowspan="2" |{{M|L}}<br/>(Measure Theory<br/>/<br/>Functional Analysis)
    2 KB (260 words) - 21:46, 20 December 2016
  • Real line
    {{Definition|Topology|Number Theory|Analysis|Functional Analysis|Metric Space}}
    107 B (13 words) - 21:33, 26 February 2017
  • List of topological properties
    {{Definition|Topology|Metric Space|Functional Analysis}}
    4 KB (630 words) - 19:33, 16 February 2017
  • Closure (topology)
    {{Definition|Topology|Real Analysis|Functional Analysis}}
    111 B (15 words) - 10:40, 30 December 2016
  • The reals
    {{Definition|Analysis|Functional Analysis|Metric Space|Set Theory}}
    98 B (12 words) - 21:36, 26 February 2017
  • C(X,Y)
    {{Definition|Topology|Functional Analysis|Analysis}}
    125 B (14 words) - 05:55, 1 January 2017
  • A compact and convex subset of Euclidean n-space with non-empty interior is a closed n-cell and its interior is an open n-cell/Statement
    {{Theorem Of|Topology|Algebraic Topology|Analysis}}
    2 KB (323 words) - 20:14, 14 January 2017
  • A compact and convex subset of Euclidean n-space with non-empty interior is a closed n-cell and its interior is an open n-cell
    {{Theorem Of|Topology|Algebraic Topology|Analysis}}
    443 B (63 words) - 20:17, 14 January 2017
  • Closed interval
    {{Definition|Functional Analysis|Analysis|Metric Space|Topology}}
    1 KB (233 words) - 14:19, 19 January 2017
  • The ell p spaces
    {{Definition|Functional Analysis|Analysis|Metric Space}}
    2 KB (296 words) - 14:30, 26 January 2017
  • Convex set
    {{Definition|Analysis|Functional Analysis}}
    799 B (143 words) - 11:27, 9 February 2017
  • Convex
    {{Definition|Analysis|Functional Analysis|Combinatorial Optimisation|Convex Optimisation}}
    532 B (92 words) - 14:50, 9 February 2017
  • Convex function
    {{Definition|Analysis|Functional Analysis|Combinatorial Optimisation|Convex Optimisation}}
    1 KB (224 words) - 10:54, 10 February 2017
  • Epigraph
    {{Definition|Analysis|Functional Analysis|Real Analysis|Convex Optimisation|Combinatorial Optimisation}}
    674 B (114 words) - 11:04, 10 February 2017
  • Convex hull
    {{Definition|Convex Optimisation|Functional Analysis|Analysis|Simplicial Homology|Singular Homology}}
    822 B (134 words) - 15:54, 12 February 2017
  • For a vector subspace of a topological vector space if there exists a non-empty open set contained in the subspace then the spaces are equal
    {{Theorem Of|Functional Analysis|Topology|Linear Algebra|Abstract Algebra}}
    924 B (140 words) - 17:51, 16 February 2017
  • A proper vector subspace of a topological vector space has no interior
    {{Theorem Of|Functional Analysis|Linear Algebra|Topology}}
    2 KB (415 words) - 17:49, 16 February 2017
  • Doctrine:K (field)
    Large swaths of functional analysis deal with something over either the reals or the complex numbers. {{M|\math * [[Books:Functional Analysis - Volume 1: A gentle introduction - Dzung Minh Ha]]
    622 B (94 words) - 18:30, 16 February 2017
  • Interior (topology)
    {{Definition|Topology|Metric Space|Functional Analysis}}
    2 KB (328 words) - 20:10, 16 February 2017
  • The interior of a set in a topological space is equal to the union of all interior points of that set
    {{Theorem Of|Topology|Functional Analysis|Metric Space}}
    550 B (77 words) - 20:15, 16 February 2017
  • Intermediate value theorem
    ***#*** We can perform the rest of the analysis using [[case analysis]] ...not it is a singleton, we didn't do this to keep the "purity" of the case analysis</ref>
    5 KB (979 words) - 17:35, 17 February 2017
  • The real line
    {{Definition|Real Analysis|Functional Analysis|Analysis|Topology|Metric Space}}
    591 B (91 words) - 17:50, 17 February 2017
  • Open neighbourhoods
    {{Definition|Topology|Metric Space|Functional Analysis|Analysis}}
    98 B (10 words) - 22:45, 22 February 2017
  • Topology induced by the metric
    {{Definition|Topology|Metric Space|Functional Analysis|Analysis}}
    108 B (13 words) - 21:13, 26 February 2017
  • Borel sigma-algebra of the real line
    {{Definition|Measure Theory|Analysis|Functional Analysis}} {{Theorem Of|Measure Theory|Analysis|Functional Analysis}}
    4 KB (712 words) - 15:48, 27 February 2017
  • Notes:Simple function approximation to a numerical function
    {{Notes|Measure Theory|Analysis|Real Analysis}}
    892 B (132 words) - 15:30, 3 March 2017
  • A sequence consisting of the nth terms of the sequences in a Cauchy sequence of elements in any little-L space is itself a Cauchy sequence of complex numbers
    {{Theorem Of|Functional Analysis|Analysis}}
    1 KB (238 words) - 17:52, 18 March 2017
  • The little-L spaces are complete
    {{Theorem Of|Analysis|Functional Analysis}}
    93 B (12 words) - 18:39, 18 March 2017
  • The little-L(C) spaces are complete
    {{Theorem Of|Analysis|Functional Analysis}}
    1 KB (236 words) - 19:03, 18 March 2017
  • Metrically bounded set
    {{Definition|Analysis|Topology|Functional Analysis|Metric Space}}
    3 KB (673 words) - 23:10, 18 March 2017
  • Metrics
    {{Definition|Analysis|Metric Space|Topology|Functional Analysis|Real Analysis}}
    100 B (11 words) - 23:34, 18 March 2017
  • A set is bounded if and only if for all points in the space there is a positive real such that the distance from that point to any point in the set is less than the positive real
    {{Theorem Of|Analysis|Functional Analysis|Metric Space|Topology}}
    6 KB (1,092 words) - 00:41, 19 March 2017
  • If two charts are smoothly compatible with an atlas then they are smothly compatible with each other
    ...charts]], {{ie}} that the {{link|transition maps|chart}} are {{link|smooth|analysis}} (in the usual {{M|\mathbb{R}^n}} sense), that is to say that: ...ough {{M|V\cap W}} would be empty of course.</ref> is [[smooth in the real analysis sense]]
    6 KB (1,182 words) - 13:38, 1 April 2017
  • Example:Smooth map between the real line and the circle (considered as smooth manifolds)
    ***#** We can preform a little bit of analysis (which isn't really needed) to tidy this up as:
    4 KB (757 words) - 13:25, 2 April 2017
  • If an inner product is non-zero then both arguments are non-zero
    {{Theorem Of|Functional Analysis|Analysis|Real Analysis|Complex Analysis}}
    1 KB (181 words) - 23:40, 7 April 2017
  • The closure of a linear subspace of a normed space is a linear subspace
    {{Theorem Of|Linear Algebra|Functional Analysis|Analysis|Topology}}
    1 KB (152 words) - 02:48, 7 April 2017
  • Given a Hilbert space and a non-empty, closed and convex subset then for each point in the space there is a closest point in the subset
    {{Theorem Of|Functional Analysis|Analysis|Complex Analysis|Real Analysis|Metric Space|Topology}}
    3 KB (592 words) - 00:52, 7 April 2017
  • For any vector subspace of a Hilbert space the orthogonal complement and the closure of that subspace form a direct sum of the entire space
    {{Theorem Of|Functional Analysis|Analysis}}
    3 KB (633 words) - 04:07, 8 April 2017
  • Orthogonal complement
    {{Definition|Functional Analysis|Analysis|Linear Algebra}}
    2 KB (278 words) - 04:07, 8 April 2017
  • Orthogonal vectors
    {{Definition|Linear Algebra|Functional Analysis|Analysis|Abstract Algebra}}
    685 B (103 words) - 04:11, 8 April 2017
  • Uniformly continuous
    {{Definition|Metric Space|Topology|Functional Analysis|Analysis|Real Analysis}}
    112 B (12 words) - 20:27, 9 April 2017
  • Distance from a point to a set
    {{Definition|Metric Space|Functional Analysis|Analysis}}
    1,017 B (196 words) - 20:28, 9 April 2017
  • The norm of a space is a uniformly continuous map with respect to the topology it induces
    {{Theorem Of|Metric Space|Functional Analysis|Analysis|Real Analysis}}
    4 KB (687 words) - 20:59, 9 April 2017
  • Square root
    {{Definition|Complex Analysis|Numerical Analysis|Analysis|Real Analysis}}
    858 B (151 words) - 05:22, 10 April 2017
  • Square root (real function)
    {{Definition|Elementary things|Pre-requisites of mathematics|Analysis|Real Analysis}}
    2 KB (408 words) - 05:46, 10 April 2017
  • Monotonicity of the integral of non-negative extended-real-valued measurable functions with respect to a measure
    {{Theorem Of|Measure Theory|Real Analysis|Analysis|Functional Analysis}}
    3 KB (623 words) - 19:41, 14 April 2017
  • Monotone convergence theorem for non-negative numerical measurable functions
    {{Theorem Of|Measure Theory|Functional Analysis|Analysis}}
    514 B (74 words) - 08:30, 17 April 2017
  • C( )0,1( ,R) is not complete when considered with the L^1 norm
    {{Theorem Of|Functional Analysis|Analysis}}
    2 KB (353 words) - 18:15, 23 April 2017
  • Monotone convergence theorem for non-negative numerical measurable functions/Statement
    {{Theorem Of|Measure Theory|Analysis|Functional Analysis}}
    2 KB (415 words) - 08:29, 17 April 2017
  • Measurable functions
    {{Definition|Measure Theory|Analysis}}
    72 B (7 words) - 08:29, 17 April 2017
  • Uniform continuity
    {{Definition|Metric Space|Topology|Analysis|Functional Analysis}}
    998 B (168 words) - 21:14, 8 April 2017
  • Graph
    {{Definition|Real Analysis|Analysis|Manifolds|Topological Manifolds|Topology|Discrete Mathematics|Set Theory}}
    650 B (103 words) - 22:35, 4 June 2017
  • Cauchy-Schwarz inequality for inner product spaces
    {{Theorem Of|Functional Analysis|Analysis|Real Analysis|Topology|Metric Space}}
    6 KB (1,279 words) - 13:00, 4 April 2017
  • The zero-to-the-power-of-zero problem
    [[Category:Real Analysis]][[Category:Problems]]
    1 KB (146 words) - 21:09, 30 November 2017
  • Geometric series
    {{Theorem Of|Analysis|Real Analysis}} {{Definition|Analysis|Real Analysis}}
    577 B (102 words) - 15:08, 5 October 2017
  • Geometric progression
    {{Definition|Analysis|Real Analysis}}[[Category:First-year friendly]]
    3 KB (494 words) - 23:08, 6 October 2017
  • Series
    {{Definition|Real Analysis|Analysis}}
    410 B (62 words) - 12:41, 5 October 2017
  • Geometric sequence
    {{Definition|Analysis|Real Analysis}}
    73 B (7 words) - 12:43, 5 October 2017
  • Statistical independence
    Main reference: {{rMSADAR}} - Mathematical Statistics and Data Analysis - 2nd edition - John A. Rice [[User:Alec|Alec]] ([[User talk:Alec|talk]])
    2 KB (372 words) - 13:47, 17 October 2017
  • Common integrals table
    [[Category:Real Analysis|Analysis|Integration]][[Category:Index]]
    805 B (135 words) - 08:11, 11 November 2017
  • Workings of the Enigma machines
    ...machine, just think of it as having an empty plugboard for the purposes of analysis.
    5 KB (834 words) - 14:25, 15 December 2017
  • Alec's taxonomy of units
    There are also questions about what can dimensional analysis yield as clues? For example can we have a not-dimensionless unit that is ju
    4 KB (592 words) - 07:29, 11 December 2017
  • Floor function
    {{Definition|Analysis|Real Analysis}}
    2 KB (377 words) - 21:20, 21 January 2018
  • Notes:Distribution of the sample median
    ===Analysis=== ...t(\int^{\Min{r,x_3} }_{-\infty}f(x_2)F(x_2) \d x_2\right)\d x_3}}, by case analysis:
    11 KB (2,371 words) - 17:21, 17 December 2017
  • Complex functionals
    {{Definition|Complex Analysis|Functional Analysis|Analysis|Linear Algebra}}
    108 B (11 words) - 15:11, 15 December 2017
  • Connected topological space
    {{Definition|Topology|Metric Space|Analysis}}
    80 B (8 words) - 15:12, 15 December 2017
  • Usual topology of the reals
    {{Requires references|Topology|Metric Space|Functional Analysis|Real Analysis}} {{Definition|Topology|Metric Space|Analysis|Real Analysis}}
    900 B (135 words) - 15:19, 15 December 2017
  • Modulus operation
    {{Definition|Analysis|Real Analysis|Complex Analysis}}
    83 B (9 words) - 17:03, 7 January 2018
  • Absolute value (function)
    {{Definition|Analysis|Real Analysis|Complex Analysis}}
    83 B (9 words) - 17:04, 7 January 2018
  • Modulo operation
    {{Definition|Number Theory|Analysis|Set Theory}}
    986 B (148 words) - 17:48, 7 January 2018
  • Modulo operator
    {{Definition|Number Theory|Analysis|Set Theory}}
    79 B (9 words) - 17:47, 7 January 2018
  • Mdm of the Binomial distribution
    Case analysis:
    2 KB (282 words) - 01:32, 12 January 2018
  • Abs (function)
    {{Definition|Real Analysis|Analysis|Complex Analysis}}
    83 B (9 words) - 12:29, 8 January 2018
  • Floor (function)
    {{Definition|Analysis|Real Analysis}}
    66 B (7 words) - 13:14, 8 January 2018
  • Notes:Statistical test results
    ==Analysis== : Here I document a form of analysis I like to apply in some areas of statistics and probability, it's not named
    4 KB (859 words) - 09:17, 29 January 2018
  • Integers
    {{Definition|Abstract Algebra|Number Theory|Real Analysis|Elementary Set Theory|Set Theory}}
    119 B (15 words) - 22:40, 6 February 2018
  • The integers
    {{Definition|Abstract Algebra|Number Theory|Real Analysis|Elementary Set Theory|Set Theory}}
    629 B (90 words) - 13:04, 10 February 2018
  • 2-Dimensional rotation matrix
    {{Definition|Linear Algebra|Computer Graphics|Real Analysis}}
    2 KB (315 words) - 08:07, 3 April 2018
  • The dimensions of energy
    [[Category:Physics]][[Category:Dimensional Analysis]]
    840 B (152 words) - 01:06, 22 June 2018
  • Minimum
    {{Definition|Analysis|Real Analysis|Order Theory|Measure Theory|Probability|Statistics}}
    121 B (13 words) - 07:21, 28 July 2018
  • Minimum function
    ** We include {{M|\alpha}} to make the cases in analysis more explicit (as this is a [[:Category:First-year friendly]] page, meaning {{Definition|Analysis|Real Analysis|Measure Theory|Probability|Statistics|Order Theory}}<!-- TODO XXX Check the
    3 KB (473 words) - 07:53, 28 July 2018
  • Rooted vector space
    * This also has applications to [[dimensional analysis]] hopefully too (see: ''[[Alec's taxonomy of units]]'' for some initial wor
    386 B (52 words) - 11:47, 5 November 2018
  • Line
    {{Definition|Analysis|Real Analysis|Topology|Functional Analysis|Linear Algebra}}
    5 KB (930 words) - 13:00, 14 December 2018

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