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• Span, linear independence, linear dependence, basis and dimension
  2 KB (330 words) - 18:07, 25 April 2015
• Given a topological manifold of dimension 2 or more and points p1, p2 and q where q is neither p1 nor p2 then a path from p1 to p2 is path-homotopic to a path that doesn't go through q
  {{DISPLAYTITLE:Given a topological manifold of dimension 2 or more and points {{M|p_1}}, {{M|p_1}} and {{M|q}} where {{M|q}} is neit For a [[topological manifold]], {{M|M}}, of [[dimension (manifold)|dimension]] no more than {{M|2}}, points {{M|p_1,p_2,q\in M}} such that {{M|q\ne p_1}
  954 B (165 words) - 11:57, 10 May 2016
• Locally euclidean of dimension n
  #REDIRECT [[Locally Euclidean topological space of dimension n]]
  137 B (15 words) - 12:37, 21 February 2017
• Locally Euclidean of dimension n
  #REDIRECT [[Locally Euclidean topological space of dimension n]]
  137 B (15 words) - 12:38, 20 February 2017
• Locally Euclidean topological space of dimension n
  {{DISPLAYTITLE:Locally Euclidean topological space of dimension {{N}}}} * I would have thought that a "locally euclidean of dimension n" space is really just something such that there exists an {{N}} for all p
  2 KB (393 words) - 12:40, 21 February 2017

Page text matches

• Vector space
  * [[Span, linear independence, linear dependence, basis and dimension]]
  2 KB (421 words) - 16:30, 23 August 2015
• Basis and coordinates
  Suppose we have a [[Span, linear independence, linear dependence, basis and dimension#Basis|Basis]], a finite one, <math>\{b_1,...,b_n\}</math>, a point {{M|p}}
  9 KB (1,525 words) - 16:30, 23 August 2015
• Measure Theory
  ..., for example consider the ring of all half-open-half-closed rectangles of dimension {{M|n}}, call this <math>\mathcal{J}^n</math>
  4 KB (733 words) - 01:41, 28 March 2015
• Manifolds
  A manifold has dimension {{M|n}} if all charts have dimension {{M|n}}
  2 KB (276 words) - 05:59, 7 April 2015
• Topological manifold
  We say {{M|M}} is a ''topological manifold of dimension {{M|n}}'' or simply ''an {{M|n-}}manifold'' if it has the following propert # {{M|M}} is locally Euclidean of dimension {{M|n}} - each point of {{M|M}} has a neighbourhood that his [[Homeomorphis
  1 KB (236 words) - 01:13, 6 April 2015
• Chart
  ...hart - or just chart on a [[Topological manifold|topological manifold]] of dimension {{M|n}} is a pair {{M|(U,\varphi)}}<ref>John M Lee - Introduction to smooth
  2 KB (322 words) - 06:32, 7 April 2015
• Smooth map
  ...M|(M,\mathcal{A})}} and {{M|(N,\mathcal{B})}} (of not necessarily the same dimension) is said to be smooth<ref>Introduction to smooth manifolds - John M Lee - S
  1 KB (235 words) - 21:37, 14 April 2015
• Notes:Pick function
  The map Ndc looses a dimension, we only know the ratios of x,y,z compared to w, we do not know w.
  4 KB (686 words) - 01:43, 15 September 2015
• Given a topological manifold of dimension 2 or more and points p1, p2 and q where q is neither p1 nor p2 then a path from p1 to p2 is path-homotopic to a path that doesn't go through q
  {{DISPLAYTITLE:Given a topological manifold of dimension 2 or more and points {{M|p_1}}, {{M|p_1}} and {{M|q}} where {{M|q}} is neit For a [[topological manifold]], {{M|M}}, of [[dimension (manifold)|dimension]] no more than {{M|2}}, points {{M|p_1,p_2,q\in M}} such that {{M|q\ne p_1}
  954 B (165 words) - 11:57, 10 May 2016
• Notes:Differential (manifolds)
  *# [[Locally Euclidean of dimension n|Locally Euclidean of dimension {{n}}]] - {{M|1=\forall p\in M\exists U\in\mathcal{J}\exists\varphi:U\right
  4 KB (716 words) - 14:24, 16 May 2016
• Notes:Dual basis
  ...'' [[vector space]] over the [[field]], {{M|\mathcal{K} }}, suppose it has dimension {{M|n\in\mathbb{N} }}.
  5 KB (1,020 words) - 08:43, 12 August 2016
• Notes:Advanced Linear Algebra - Roman/Chapter 1
  ...rect seems to mean like "the sum of the dimensions of the subspaces is the dimension of the result" - kind of - for infinite cases this phrasing obviously doens
  8 KB (1,463 words) - 14:35, 13 August 2016
• Semi-ring of sets
  * [[Lebesgue pre-measure on a semi-ring]] - in one dimension the semi-ring, {{M|\mathscr{J}^1}}, here is the collection of all half-open
  3 KB (508 words) - 17:25, 18 August 2016
• Notes:Homology
  *#** The dimension of the kernel is {{M|2}} so the dimension of the image is {{M|2}} also! *** Clearly the dimension is 2.
  6 KB (897 words) - 07:30, 15 October 2016
• Total derivative
  If the [[vector spaces]] {{M|U}} and {{M|V}} are finite {{link|dimension|vector space|al}} then recall [[all norms on finite dimensional vector spac
  2 KB (313 words) - 01:27, 15 November 2016
• Characteristic property of the tensor product/Statement
  ...d]] and let {{M|\big((V_i,\mathbb{F})\big)_{i\eq 1}^k}} be a family of ''[[dimension (vector space)|finite dimensional]]'' [[vector spaces]] over {{M|\mathbb{F}
  2 KB (268 words) - 22:07, 20 December 2016
• Basis for the tensor product/Statement
  ...d]] and let {{M|\big((V_i,\mathbb{F})\big)_{i\eq 1}^k}} be a family of ''[[dimension (vector space)|finite dimensional]]'' [[vector spaces]]. Let {{M|n_i:\eq\te
  972 B (177 words) - 23:56, 6 December 2016
• Example:Canonical linear isomorphism between a one dimensional vector space and its field
  ...[field]] and let {{M|(V,\mathbb{F})}} be a [[vector space]]. If the {{link|dimension|vector space}} of {{M|V}} is {{M|1}} then:
  2 KB (320 words) - 05:44, 7 December 2016
• Tensor product of tensors
  ...xt{lots of }V};\mathbb{F})}} in mine for vec space {{M|(V,\mathbb{F})}} of dimension {{M|n}}, then:
  3 KB (497 words) - 21:58, 22 December 2016
• CW-complex
  ...] is mapped into a finite [[union]] of [[open n-cell|open {{N|cells}}]] of dimension strictly less than that of {{M|e}}
  1 KB (187 words) - 14:14, 20 January 2017
• Notes:CW-Complex
  ...record Munkres' exact phrasing</ref> a finite union of open cells, each of dimension (strictly) less than {{M|m}}
  10 KB (1,736 words) - 01:00, 23 January 2017
• Exercises:Saul - Algebraic Topology - 2/Exercise 2.5
  # Showing {{M|\mathbb{Q} }} does not have rank ("dimension" as cardinality of "basis") {{M|\ge 2}} - or an infinite basis.
  4 KB (713 words) - 12:22, 25 January 2017
• Exercises:Saul - Algebraic Topology - 3/Exercise 3.2
  ...ton}} of {{M|X}}. Which made from all the simplices involved in {{M|X}} of dimension {{M|\le n}}. So {{M|X^1}} is itself a complex made up of all the 0 and 1 si
  13 KB (2,312 words) - 06:33, 1 February 2017
• Simplex
  * '''{{link|Dimension|simplex}}:''' {{M|\text{Dim}(\sigma):\eq\vert\{a_0,\ldots,a_n\}\vert-1}}<re
  3 KB (548 words) - 14:03, 31 January 2017
• Real projective space
  ...in\mathcal{P}(\mathbb{R}^{n+1})\ \vert\ (L,\mathbb{R})\text{ is an 1-} }}[[dimension (vector space)|{{M|\text{dimensional} }}]]{{M|\text{ vector } }}[[vector su
  2 KB (289 words) - 09:08, 18 February 2017
• Abstract simplicial complex
  * We make the following definitions regarding [[dimension]] of an abstract simplicial complex: ...A\in\mathcal{S} }}, we define: {{M|\text{Dim}(A):\eq\vert A\vert-1}} - the dimension of {{M|A}} is one less than the number of items in the simplex considered a
  3 KB (428 words) - 11:54, 19 February 2017
• Locally Euclidean topological space
  : {{Caveat|Need to do locally euclidean '''of dimension {{n}}'''!}}
  4 KB (667 words) - 14:32, 20 February 2017
• Locally euclidean of dimension n
  #REDIRECT [[Locally Euclidean topological space of dimension n]]
  137 B (15 words) - 12:37, 21 February 2017
• Locally Euclidean of dimension n
  #REDIRECT [[Locally Euclidean topological space of dimension n]]
  137 B (15 words) - 12:38, 20 February 2017
• Locally Euclidean topological space of dimension n
  {{DISPLAYTITLE:Locally Euclidean topological space of dimension {{N}}}} * I would have thought that a "locally euclidean of dimension n" space is really just something such that there exists an {{N}} for all p
  2 KB (393 words) - 12:40, 21 February 2017
• Exercises:Saul - Algebraic Topology - 8/Exercise 8.5
  ...initions of [[locally euclidean of dimension n|locally euclidean (of fixed dimension)]], they vary as follows:
  7 KB (1,330 words) - 15:25, 7 March 2017
• Graph (topological manifold)
  ...fold|topological {{n|manifold}}]] (literally a [[topological manifold]] of dimension {{M|n}}) * [[Locally Euclidean of dimension n|Locally Euclidean of dimension {{n}}]] - which we will now show
  2 KB (369 words) - 12:53, 17 March 2017
• If two charts are smoothly compatible with an atlas then they are smothly compatible with each other
  ...we speak of {{M|\mathbb{R}^m}} and {{M|\mathbb{R}^n}}, this is because the dimension of [[connected components]] may vary from component to component, in this c
  6 KB (1,182 words) - 13:38, 1 April 2017
• Notes:Grid iteration
  ...y to using this system in higher dimensions as at 20 we'd increase the 3rd dimension to place our 2d grid there, see gif below]] ...higher dimensions (returning to the start, where we would increase the 4th dimension to create a distinct point, if we did so here)
  3 KB (468 words) - 19:23, 7 January 2018