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• Addition of vector spaces
  | Given <math>V_1,\cdots,V_n</math> which are [[Vector space|vector spaces]] over the same field {{M|F}}:<br/> | [[Sum of vector spaces]]
  4 KB (804 words) - 18:02, 18 March 2016
• Tensor product of vector spaces
  ...nd let {{M|\big((V_i,\mathbb{F})\big)_{i\eq 1}^k}} be a family of [[vector spaces]] over {{M|\mathbb{F} }}. Let {{M|\mathcal{F}(V_1\times\cdots\times V_k)}}
  2 KB (377 words) - 21:33, 22 December 2016
• Subtypes of topological spaces
  51 B (6 words) - 22:37, 11 July 2015
• Index of spaces
  When breaking up a term into its index key, spaces delimit the blocks, for example {{M|L_1^2}} becomes {{C|L _num:1 ^num:2}} ( ...|L(X,Y)}} (where {{M|X}} and {{M|Y}} are objects (vector spaces, or Banach spaces... ) we use the key {{C|obj}} for these. So {{M|L(X,Y)}} becomes {{C|L ( ob
  3 KB (612 words) - 21:06, 29 February 2016
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere
  Given two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and a [[linea [[Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/1 implies 2|{{M|1)\implies 2)}}]]: That {{M|L}}
  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
  Given two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and also a [[ * Let the normed spaces {{M|X}} and {{M|Y}} be given, as well as a [[linear map]] {{M|L:X\rightarro
  5 KB (1,064 words) - 02:24, 28 February 2016
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/2 implies 3
  Given two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and also a [[
  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
  Given two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and also a [[
  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
  Given two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and also a [[
  2 KB (279 words) - 01:34, 28 February 2016
• Topological spaces
  ...convenience" redirect. Writing {{C|<nowiki>[[Topological space|topological spaces]]</nowiki>}} often is annoying.
  180 B (21 words) - 21:31, 3 May 2016
• Vector spaces
  73 B (8 words) - 12:41, 15 September 2016
• Homotopy is an equivalence relation on the set of all continuous maps between spaces
  Let {{Top.|X|J}} and {{Top.|Y|K}} be [[topological spaces]]. Let {{M|A\in\mathcal{P}(X)}} be an arbitrary [[subset]] of {{M|X}}. Then
  2 KB (272 words) - 23:37, 14 October 2016
• Homotopy is an equivalence relation on the set of all continuous maps between spaces/proof
  Where we are given [[topological spaces]], {{Top.|X|J}} and {{Top.|Y|K}}, and also an arbitrary [[subset]] of {{M|X
  3 KB (533 words) - 07:33, 18 September 2016
• A topological space is disconnected if and only if it is homeomorphic to a disjoint union of two or more non-empty topological spaces
  ...joint union topology|disjoint union]] of two or more non-empty topological spaces
  833 B (126 words) - 23:15, 30 September 2016
• Metric spaces
  63 B (7 words) - 18:43, 28 October 2016
• The set of continuous functions between topological spaces
  Let {{Top.|X|J}} and {{Top.|Y|K}} be [[topological spaces]]. Then {{M|C(X,Y)}} denotes the [[set]] of all ''[[continuous]]'' [[functi ...of all linear maps]] - denote {{M|L(V,W)}}, for {{M|V}} and {{M|W}} vector spaces over the same field
  1 KB (235 words) - 05:02, 3 November 2016
• Index of spaces, sets and classes
  * [[The set of continuous functions between topological spaces]] - {{M|C(X,Y)}}
  335 B (61 words) - 05:06, 3 November 2016
• Normed spaces
  92 B (10 words) - 10:00, 11 November 2016
• The vector space of all linear maps between two spaces
  {{DISPLAYTITLE:The vector space of all linear maps between two spaces - {{M|L(U,V)}}}}{{Stub page|grade=A*|msg=Time to start committing to these} ...[field]] and let {{M|(U,\mathbb{K})}} and {{M|(V,\mathbb{K})}} be [[vector spaces]] over {{M|\mathbb{K} }}. We define:
  2 KB (400 words) - 21:16, 17 November 2016
• Set of all linear maps between spaces
  #REDIRECT [[The vector space of all linear maps between two spaces]]
  118 B (16 words) - 21:16, 17 November 2016

Page text matches

• Homeomorphism
  If {{Top.|X|J}} and {{Top.|Y|K}} are [[topological space|topological spaces]] a ''homeomorphism from {{M|X}} to {{M|Y}}'' is a{{rITTMJML}}: ...ion here. If you have a bijection, and both directions are continuous, the spaces are in no real way distinguishable.</ref> I recommend you use {{M|\cong}}.
  5 KB (731 words) - 22:58, 22 February 2017
• Topological space
  Given two ''topological spaces'', {{M|(X_1,\mathcal{J}_1)}} and {{M|(X_2,\mathcal{J}_2)}} we may be able t
  2 KB (268 words) - 13:37, 20 April 2016
• Metric space
  ...ationships between metric spaces and others see: [[Subtypes of topological spaces]]
  2 KB (336 words) - 06:07, 27 November 2015
• Continuous map
  Given two [[topological space|topological spaces]] {{M|(X,\mathcal{J})}} and {{M|(Y,\mathcal{K})}} we say that a [[map]], {{ Again, given two [[topological space|topological spaces]] {{M|(X,\mathcal{J})}} and {{M|(Y,\mathcal{K})}}, and a point {{M|x_0\in X
  6 KB (972 words) - 01:44, 14 October 2016
• Compactness
  ...ess and sequences]]''' - I think there's a different definition for metric spaces, I have not seen a proof that the metric one {{M|\implies}} this one ...pactness of subsets. Compactness is ''strictly'' a property of topological spaces.
  5 KB (828 words) - 15:59, 1 December 2015
• Quotient topology
  ...mathcal{J})}} and {{M|(Y,\mathcal{K})}} be [[Topological space|topological spaces]] and let {{M|p:X\rightarrow Y}} be a [[Surjection|surjective]] map.
  5 KB (795 words) - 13:34, 16 October 2016
• Homomorphism
  ...s of {{plural|vector space|s}} - see also: WHATEVER THE CATEGORY OF VECTOR SPACES OVER A FIELD IS CALLED! {{Stub page|grade=B|msg=Flesh out, modules, algebras, measurable spaces!}}
  4 KB (532 words) - 22:04, 19 October 2016
• Vector space
  An introduction to the important concepts of vector spaces and linear algebra may be found on the [[Basis and coordinates]] page * [[Linear map|Linear maps]] - the homomorphisms and isomorphisms of vector spaces
  2 KB (421 words) - 16:30, 23 August 2015
• Measure space
  '''Note:''' This page requires knowledge of [[Measurable space|measurable spaces]].
  1 KB (188 words) - 15:24, 21 July 2015
• Product topology
  ...l{J}_\alpha)\big)_{\alpha\in I} }} be an arbitrary family of [[topological spaces]]. The ''product topology'' is a new topological space defined on the [[set : '''Note: ''' for finite collections of topological spaces the product and [[box topology]] agree. In general however the box topology
  5 KB (871 words) - 20:32, 23 September 2016
• Function
  * If we have say two [[Topological space|topological spaces]] {{M|(X,\mathcal{J})}} and {{M|(Y,\mathcal{K})}} then we may write:
  4 KB (659 words) - 13:01, 19 February 2016
• Equivalence relation
  ...m]]'' (which is an equivalence relation on [[topological space|topological spaces]])
  3 KB (522 words) - 15:18, 12 February 2019
• Bilinear map
  A bilinear map combines elements from 2 [[Vector space|vector spaces]] to yield and element in a third (in contrast to a [[Linear map|linear map ...han mapping to a vector space {{M|W}} it maps to the field that the vector spaces {{M|U}} and {{M|V}} are over (which in this case was {{M|F}})<ref name="Rom
  4 KB (682 words) - 15:44, 16 June 2015
• Norm
  ...dering would you use? The [[canonical]] ordering used for the product of 2 spaces ({{M|\mathbb{R}\times\mathbb{R} }} in this case) is the [[Lexicographic ord ==Relation to various [[subtypes of topological spaces]]==
  6 KB (1,026 words) - 20:33, 9 April 2017
• Absolute value
  ...gle inequality]], link to [[norm]] of reals, link to [[metric space|metric spaces]]}}
  795 B (110 words) - 18:15, 18 March 2016
• Cauchy-Schwarz inequality
  :: {{Highlight|Update: [[Cauchy-Schwarz inequality for inner product spaces]] is a proof of the second form - note that {{M|\Vert x\Vert:\eq\sqrt{\lang
  3 KB (609 words) - 13:04, 4 April 2017
• Index of notation
  ! [[Index of spaces]] | Spaces
  9 KB (1,490 words) - 06:13, 1 January 2017
• Linear isometry
  Suppose {{M|U}} and {{M|V}} are [[Norm|normed]] [[Vector space|vector spaces]] with the norm <math>\|\cdot\|_U</math> and <math>\|\cdot\|_V</math> respe ==Isometric normed vector spaces==
  1 KB (206 words) - 11:23, 12 May 2015
• Sequential compactness
  Sequential compactness extends this notion to general topological spaces.
  1 KB (228 words) - 15:37, 24 November 2015
• Cauchy criterion for convergence
  ...untered it with sequences on {{M|\mathbb{R} }} - there are of course other spaces! As such this page is being refactored.
  898 B (145 words) - 15:26, 24 November 2015