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{{wikibooks|Topology/Topological Spaces}} {{en-noun|-}} ...

{{en-noun|initial topologies}} ...functions <math>f_i: X\to M_i</math>, the initial topology is the coarsest topology on <math>X</math> such that all <math>f_i</math> are continuous.}} ...

{{en-noun|final topologies}} ...of functions <math>f_i: M_i\to X</math>, the final topology is the finest topology on <math>X</math> such that all <math>f_i</math> are continuous.}} ...

{{en-noun}} ...from one [[topological space]] to another one, such that the latter one's topology has the property that if the [[inverse image]] (under the said function) of ...

Along with the closely related concept of {{m|en|Alexandrov-discrete space}}, after Russian mathematician {{w|Pavel Sergeyev {{en-noun}} ...

{{en-noun}} # {{lb|en|math|given some [[set]] and an [[equivalence relation]] on that set}} the s ...

{{en-noun}} ...a given set of [[topological space]]s and is the largest (most inclusive) topology that preserves the continuity of each contributing space as represented in ...

{{en-noun}} # {{lb|en|algebraic geometry}} Originally, a [[topology]] applicable to [[algebraic variety|algebraic varieties]], such that the [[ ...

{{en-noun}} # {{lb|en|analysis}} In the abstract [[metric space]] of all [[compact]] subsets of < ...

* {{audio|en|LL-Q1860 (eng)-Flame, not lame-adic.wav|a=US}} {{en-adj|-}} ...

{{en-noun}} # {{lb|en|topology}} An [[immersion]] of the [[sphere]] <math>S^2</math> in <math>\R^3</math>, ...

...n|-ad}} + {{m|en|-ic}}). Compare related {{m|en|adicity}} and Latinate {{m|en|-ary}}. ...ince <math>\mathbb{Z}_{(p)}</math> equipped with the <math>(p)</math>-adic topology passes to the ring of {{w|p-adic numbers}} under the operation of [[complet ...

{{head|en|noun|head=[[Jordan curve]] [[theorem]]}} # {{lb|en|topology}} The theorem that states that a [[simple closed curve]] ([[Jordan curve]]) ...

...{{der|en|LL.|topologia}}, from {{der|en|grc|τόπος||place, locality}} + {{m|en|-logy|-(o)logy|study of, a branch of knowledge}}. * {{IPA|en|/təˈpɒləd͡ʒi/|a=RP}} ...

{{en-noun}} # {{lb|en|topology|and|algebra}} A space obtained from another by [[identification]] of [[poin ...

From {{prefix|en|semi|topological}}. {{en-adj|-}} ...

{{en-verb|*}} # {{lb|en|transitive}} To [[finish]] by making one last addition. ...

{{en-noun}} ...natively, for a different set of axioms, the ''[[closed set]]s'');<br>{{lb|en|loosely}} the set ''X''. ...

{{en-proper noun|def=1}} # {{lb|en|topology}} A theorem which (in one of its simplest forms) states that a continuous f ...

{{en-noun|head=[[locally compact]] [[group]]}} # {{lb|en|topology}} A [[topological group]] whose underlying [[topology]] is both [[locally compact]] and [[Hausdorff]]. ...