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Create the page "C(X,C)" on this wiki! See also the search results found.

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• C(I,X)
  {{DISPLAYTITLE:{{M|C([0,1],X)}}}} ...=I:=[0,1]\subset\mathbb{R} }} - the [[closed unit interval]]. Then {{M|C(I,X)}} denotes the [[set of continuous functions]] between the interval, consid
  1 KB (258 words) - 05:08, 3 November 2016
• C(X,Y)
  125 B (14 words) - 05:55, 1 January 2017

Page text matches

• Topology
  ...Should be easy to flesh out, find some more references and demote to grade C once acceptable}} ...of {{M|X}}. This means that if {{M|U\in\mathcal{J} }} then {{M|U\subseteq X}}</ref> such that{{rITTMJML}}{{rFAVIDMH}}:
  3 KB (543 words) - 09:28, 30 December 2016
• Topological space
  {{Requires references|grade=C|Need references for larger/smaller/stronger/weaker, Check Introduction To T * Given any set {{M|X}} we can always define the following two topologies on it:
  2 KB (268 words) - 13:37, 20 April 2016
• Nabla
  <math>\nabla(\ )=\mathbf{i}\frac{\partial(\ )}{\partial x}+\mathbf{j}\frac{\partial(\ )}{\partial y}+\mathbf{k}\frac{\partial(\ )}{\p <math>\nabla\cdot\nabla(\ )=\nabla^2(\ )=\frac{\partial^2(\ )}{\partial x^2}+\frac{\partial^2(\ )}{\partial y^2}+\frac{\partial^2(\ )}{\partial z^2}<
  1 KB (245 words) - 18:35, 13 February 2015
• Connected (topology)
  Let {{Top.|X|J}} be a [[topological space]]. We say {{M|X}} is ''connected'' if{{rITTMJML}}: ...}[U\ne\emptyset\wedge V\neq\emptyset\wedge U\cap V=\emptyset\wedge U\cup V=X])}}
  5 KB (866 words) - 01:52, 1 October 2016
• Subspace topology
  ...let {{M|S}} be a subset of {{M|X}}, possibly empty, possibly equal to {{M|X}} itself</ref> be given. We can construct a new topological space, {{M|(S,\ ...|(S,\mathcal{J}_S)}} are precisely the intersection of open sets of {{Top.|X|J}} with {{M|S}}
  6 KB (1,146 words) - 23:04, 25 September 2016
• The set of all open balls of a metric space are able to generate a topology and are a basis for that topology
  ...X\rightarrow\mathbb{R}_{\ge 0} }} be a [[metric]] on that set and let {{M|(X,d)}} be the resulting [[metric space]]. Then we claim: * {{M|\mathcal{B}:\eq\left\{ B_\epsilon(x)\ \vert\ x\in X\wedge \epsilon\in\mathbb{R}_{>0}\right\} }} satisfies the condition [[topol
  4 KB (814 words) - 22:16, 16 January 2017
• Closure, interior and boundary
  ...verline{A}=\bigcap\{B\subset X|A\subset B\text{ and }B\text{ is closed in }X\}</math> ...text{Int}(A)=\bigcup\{C\subset X|C\subset A\text{ and }C\text{ is open in }X\}</math>
  1 KB (210 words) - 00:20, 9 March 2015
• Function
  * {{M|f\subseteq X\times Y}} ...imes Y}} we have {{M|1=\forall x\in X\forall y,z\in Y[(x\mathcal{R}y\wedge x\mathcal{R}z)\implies y=z]}}
  4 KB (659 words) - 13:01, 19 February 2016
• Set theory axioms
  ...{M|Y}} and every element of {{M|Y}} is also an element of {{M|X}} then {{M|X=Y}}<br/> |<math>\forall X\forall Y(\forall u(u\in X\leftrightarrow u\in Y)\rightarrow X=Y)</math>
  3 KB (619 words) - 10:25, 11 March 2015
• Relation
  ...sets{{rAPIKM}}<ref name="TAPL">Types and Programming Languages - Benjamin C. Peirce</ref>, that is: * {{M|\mathcal{R}\subseteq X\times Y}}
  4 KB (762 words) - 20:07, 20 April 2016
• Ordering
  | <math>\forall a\in A\forall b\in A\forall c\in A([aRb\wedge bRc]\implies aRc)</math> ...=\mathbb{N} }} then <math>a\le b\wedge b\le c\iff a\le b\le c\implies a\le c</math>
  5 KB (1,006 words) - 13:21, 1 January 2016
• Equivalence relation
  ...{{M|X}}<ref group="Note">This terminology means {{M|\sim \subseteq X\times X}}, as described on the [[relation]] page.</ref> is an ''equivalence relatio ...|\forall x\in X[(x,x) \in \sim]}}. Which we write {{M|\forall x\in X[x\sim x]}}.
  3 KB (522 words) - 15:18, 12 February 2019
• Norm
  ...of {{M|\Vert\cdot\Vert}} could be in {{M|\mathbb{C} }} then the {{M|\Vert x\Vert\ge 0}} would make no sense. What ordering would you use? The [[canonic # <math>\forall x\in V\ \|x\|\ge 0</math>
  6 KB (1,026 words) - 20:33, 9 April 2017
• Cauchy-Schwarz inequality
  * {{MM|1=\vert\langle x,y\rangle\vert\le\Vert x\Vert \Vert y\Vert}} - the rare but more general ...a proof of the second form - note that {{M|\Vert x\Vert:\eq\sqrt{\langle x,x\rangle} }} is the [[norm induced by the inner product]] [[User:Alec|Alec]]
  3 KB (609 words) - 13:04, 4 April 2017
• Index of notation
  ...to {{M|\mathbb{R} }} - this is unlikely to be given any other way because "C" is for continuous. | {{M|\mathbb{S}^n}}, {{M|l_2}}, {{M|\mathcal{C}[a,b]}}
  9 KB (1,490 words) - 06:13, 1 January 2017
• Basis and coordinates
  ...e, so the coordinate {{M|(x,y)}} is on our paper, and {{M|(x,y)'}} or {{M|(x',y')}} is on their paper. ...[Linear map|linear transform]]? Well recall to be linear <math>T(ax+by)=aT(x)+bT(y)</math>
  9 KB (1,525 words) - 16:30, 23 August 2015
• Group
  ||<math>\forall a,b,c\in G:[(a*b)*c=a*(b*c)]</math> ...*}} is [[Associative|associative]], because of this we may write <math>a*b*c</math> unambiguously.
  7 KB (1,332 words) - 07:17, 16 October 2016
• Cardinality
  ...be injective, but would not be surjective if <math>\exists x(x\in C\wedge x\notin B)</math>, thus not bijective.<ref>p65 - Introduction to Set Theory,
  2 KB (327 words) - 10:25, 12 March 2015
• Algebra of sets
  ...roup="Note">Recall {{M|1=A^C:=X-A}} - the [[complement]] of {{M|A}} in {{M|X}}</ref> ...} in {{M|\mathcal{A} }} the [[complement]] of {{M|A}} (with respect to {{M|X}}) is also in {{M|\mathcal{A} }}
  3 KB (507 words) - 18:43, 1 April 2016
• Sigma-algebra
  # {{M|X\in\mathcal{A} }} as {{M|\emptyset^C\in\mathcal{A} }} :: As {{M|1=A-B=(A^c\cup B)^c}} and a {{sigma|algebra}} is closed under complements and unions, this show
  8 KB (1,306 words) - 01:49, 19 March 2016