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• 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
  ...elements in any {{M|\ell^p}} space is itself a Cauchy sequence of complex numbers}} : This theorem is a [[precursor]] to [[the little-L spaces are complete]]
  1 KB (238 words) - 17:52, 18 March 2017

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• Examples of rings
  The integers, {{M|\mathbb{Z} }} with the usual operations of addition and multiplication (usual meaning 5+4 = 9, 5*4 The real numbers, {{M|\mathbb{R} }} is a commutative ring with unity too, and {{M|\mathbb{Z}
  2 KB (269 words) - 17:11, 19 May 2015
• Monomial
  ...|polynomial]] consisting of "no {{M|+}} sign" if you will (unless it is in the coefficient), for example: ...M|(12+2j)xy^2z}} is also a monomial (just over the [[Complex field|complex numbers]])
  942 B (143 words) - 13:49, 17 June 2015
• Space of square-summable sequences
  ...[[Countable|countable]]) [[Sequence|sequences]] of either complex, or real numbers<ref name="FA">Functional Analysis - George Bachman and Lawrence Narici</ref With the property of:
  893 B (141 words) - 15:47, 12 July 2015
• Notes:Spherical coordinates
  ...o-load-a-spherical-planet-and-its-regions this question] and not a part of the site, I needed math-markup}} ..., yet to someone standing on it it is rather plane-like. This was actually the subject of some dispute many years ago!
  10 KB (1,899 words) - 18:48, 23 September 2015
• Topological vector space
  {{Stub page|msg=Find out if the space must be real, although it looks like it must be. Also find another re ...logy]] on {{M|X}} so that {{Top.|X|J}} is a [[topological space]]. We call the [[tuple]]:
  2 KB (383 words) - 14:03, 16 February 2017
• The set of continuous functions between topological spaces
  ...''[[continuous]]'' [[functions]] from {{M|X}} to {{M|Y}}, with respect to the {{plural|topolog|y|ies}}: {{M|\mathcal{J} }} and {{M|\mathcal{K} }}. *** [[The fundamental group]]
  1 KB (235 words) - 05:02, 3 November 2016
• Total derivative
  ...tal/partial terminology, as total/partial are common. As I need to rewrite the current strong page anyway, I've started here [[User:Alec|Alec]] ([[User ta ...the same [[field]] (either both [[real numbers|real]] or [[complex numbers|complex]]), let {{M|A\in\mathcal{P}(U)}} be an arbitrary [[subset of]] {{M|U}} and
  2 KB (313 words) - 01:27, 15 November 2016
• Index of notation for sets of continuous maps/Index
  ...for [[topological spaces]] {{Top.|X|J}} and {{Top.|Y|K}}, {{M|C(X,Y)}} is the [[set]] of all [[continuous maps]] between them. # [[C(X,R)|{{M|C(X,\mathbb{R})}}]] - The ''[[algebra]]'' of all {{plural|real functional|s}} on {{M|X}}. {{M|\mathbb
  2 KB (463 words) - 06:20, 1 January 2017
• Notes:Stone-Weierstrass theorem
  ...cally equivalent to the form in the lecture notes. I document them here in the hope of showing it to someone who can tell me what form to commit to. ...he [[field]] that is either the [[complex numbers]], {{M|\mathbb{C} }}, or the [[reals]], {{M|\mathbb{R} }}</ref> such that:
  4 KB (791 words) - 13:29, 27 January 2017
• Convex set
  ...bb{K} }} which is either [[the reals]], {{M|\mathbb{R} }} or the [[complex numbers]], {{M\mathbb{C} }} and let {{M|C\in\mathcal{P}(X)}} be given. Then we say ...the (closed) line between {{M|x}} and {{M|y}} by [[abuse of notation]] for the notation of a [[closed interval]]
  799 B (143 words) - 11:27, 9 February 2017
• Notes:Functional Analysis II
  ...e [[field]] of [[the reals]], {{M|\mathbb{R} }}, or the field of [[complex numbers]], {{M|\mathbb{C} }} * Suppose that {{M|N:X\rightarrow \mathbb{R} }} satisfies the following three properties:
  4 KB (818 words) - 12:00, 9 February 2017
• Doctrine:K (field)
  ...either [[the reals]], so {{M|\mathbb{K}:\eq\mathbb{R} }}, or [[the complex numbers]], so {{M|\mathbb{K}:\eq\mathbb{C} }} ...te - unless otherwise stated - the case where either may be substituted by the reader.
  622 B (94 words) - 18:30, 16 February 2017
• Doctrine:K (topological space)
  {{M|K}} shall denote the (underlying set) of any [[topological space]] which is {{link|compact|topol ...ntinuous functions from a compact space to either the reals or the complex numbers]]
  518 B (76 words) - 18:36, 16 February 2017
• Doctrine:K
  ...athbb{K} }} may be either [[the reals|{{M|\mathbb{R} }}]] or [[the complex numbers|{{M|\mathbb{C} }}]] ...' [[topological space]], {{M|(K,\mathcal{J})}} where {{M|\mathcal{J} }} is the associated [[topology]]
  617 B (92 words) - 18:42, 16 February 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
  ...elements in any {{M|\ell^p}} space is itself a Cauchy sequence of complex numbers}} : This theorem is a [[precursor]] to [[the little-L spaces are complete]]
  1 KB (238 words) - 17:52, 18 March 2017
• K (field)
  ...re that the doctrine page lists references that this page does, as they're the same thing!}} ...he [[field of real numbers]], {{M|\mathbb{R} }}, or the [[field of complex numbers]], {{M|\mathbb{C} }}.
  2 KB (323 words) - 03:54, 8 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
  ...a [[Hilbert space]] and let {{M|L\subseteq X}} be a [[vector subspace]] of the [[vector space]] {{M|(X,\mathbb{K})}}, then{{rW2014LNFARS}}: ...induced by the norm]] {{M|\Vert\cdot\Vert}} which is the [[norm induced by the inner product]] {{M|\langle\cdot,\cdot\rangle}}</ref>
  3 KB (633 words) - 04:07, 8 April 2017
• Square root
  {{Stub page|grade=A|msg=Complex viewpoint would be good, maybe a numerical one for approximating maybe?}} ...or {{M|i}} (this site uses {{M|j}}), this forms the basis of the [[complex numbers]]
  858 B (151 words) - 05:22, 10 April 2017