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- ...topology)|continuous maps]] <math>f: X \to Y</math>, and while equivariant topology also considers such maps, there is the additional constraint that each map ...to any symmetry possessed by both spaces. A famous theorem of equivariant topology is the [[Borsuk–Ulam theorem]], which asserts that every <math>\mathbf{Z}_2 ...6 KB (940 words) - 15:37, 4 October 2024
- ...ogy''' is a certain [[Grothendieck topology]], which is finer than [[étale topology]]. Its main use is to define the cohomology of an [[algebraic stack]] with ...he cohomology of <math>B\mathbb{G}_m</math> should be defined using smooth topology for formulae like [[Behrend's fixed point formula]] to hold. ...1 KB (194 words) - 07:11, 26 June 2024
- ...e= 45|pages=243–327}}</ref> Collapses find applications in [[Computational topology#Computational homology|computational homology]].<ref>{{Cite book|title=Comp ...ing]]'s [[house with two rooms]] and [[Christopher Zeeman]]'s [[Dunce hat (topology)|dunce hat]]; they are [[contractible]] (homotopy equivalent to a point), b ...3 KB (384 words) - 18:06, 7 February 2023
- {{Short description|Topology on the space of semimartingales}} ...urnal|first1=Constantinos|last1=Kardaras|title=On the closure in the Emery topology of semimartingale wealth-process sets|journal=Annals of Applied Probability ...2 KB (310 words) - 05:58, 27 September 2024
- ...name{Spec}(A)</math> is a [[closed map]] with respect to the constructible topology. ...ral, the constructible topology is a [[finer topology]] than the [[Zariski topology]], and the two topologies coincide if and only if <math>A / \operatorname{n ...2 KB (316 words) - 23:51, 12 August 2023
- {{DISPLAYTITLE:''h'' topology}} In [[algebraic geometry]], the '''''h'' topology''' is a [[Grothendieck topology]] introduced by [[Vladimir Voevodsky]] to study the [[homology theory|homol ...11 KB (1,657 words) - 05:09, 16 November 2024
- In [[topology]], a branch of [[mathematics]], a '''graph''' is a [[topological space]] wh Thus, in particular, it bears the [[quotient topology]] of the [[Set (mathematics)|set]] ...4 KB (564 words) - 07:55, 21 February 2024
- ...eger]]s greater than or equal to two. The divisor topology is the [[poset topology]] for the [[partial order]] relation of [[divisibility]] of integers on <ma ...th>n = 2,3,...</math> form a [[basis (topology)|basis]] for the '''divisor topology'''<ref name="CEIT">Steen & Seebach, example 57, p. 79-80</ref> on <math>X</ ...4 KB (657 words) - 22:45, 18 October 2020
- {{Short description|Analog of Grothendieck topology}} ...also sometimes also called a '''local operator''' or '''coverage''' or '''topology''' or '''geometric modality'''. They were introduced by {{harvs|txt|author ...4 KB (550 words) - 16:57, 3 February 2024
- {{Short description|Branch of topology}} '''String topology''', a branch of [[mathematics]], is the study of algebraic structures on th ...9 KB (1,380 words) - 11:03, 25 March 2024
- * {{cite book|first=Dmitry|last= Kozlov |title=Combinatorial Algebraic Topology |publisher=Springer |location=Berlin |year=2008 |isbn=978-3-540-71961-8}} [[Category:Algebraic topology]] ...3 KB (492 words) - 02:43, 13 November 2024
- ...so known as the '''universally subtrusive topology''') is a [[Grothendieck topology]] whose covers are characterized by lifting maps from [[valuation ring]]s. ...d further by {{harvtxt|Bhatt|Scholze|2017}}, who introduced the name ''v''-topology, where ''v'' stands for valuation. ...3 KB (461 words) - 18:27, 1 June 2023
- {{distinguish|Linear bus topology}} ...ogical module|topological <math>A</math>-module]] with respect to a linear topology. ...2 KB (345 words) - 11:49, 28 November 2024
- {{Short description|Example of a topology on the set of positive integers}} ...{harvs|txt|last=Appert|first=Antoine|year=1934}}, is a [[topological space|topology]] on the set {{nowrap|1=''X'' = {1, 2, 3, ...}}} of [[natural number|positi ...4 KB (608 words) - 17:02, 24 August 2024
- ...omputational topology]]'', which studies the application of computation to topology. ==Topology of lambda calculus== ...20 KB (3,257 words) - 19:42, 7 February 2025
- ...ard topology on '''R'''. It is mostly useful for counterexamples in basic topology. In particular, it provides an example of a [[Hausdorff space]] that is no ...''K-topology''' on '''R''' is the topology obtained by taking as a [[base (topology)|base]] the collection of all open intervals <math>(a,b)</math> together wi ...4 KB (585 words) - 22:59, 3 August 2024
- In [[mathematics]], particularly in [[algebraic topology]], a '''taut pair''' is a [[topological pair]] whose [[direct limit]] of [[ ...f name="auto">{{cite book |last1=Spanier |first1=Edwin H. |title=Algebraic topology |date=1966 |page=289|publisher=Springer |isbn=978-0387944265}}</ref> ...5 KB (870 words) - 00:10, 11 November 2023
- {{short description|Mathematical theory related to general topology}} ...ional sequence topology''' is an example of a [[Topological space#topology|topology]] given to the set '''R''' of [[real number]]s. ...1,018 bytes (149 words) - 00:10, 5 June 2023
- {{about|the topology of electrical circuits|the topology of polymers|Circuit topology}} ...Numerous physical layouts and circuit diagrams may all amount to the same topology. ...47 KB (7,319 words) - 06:19, 19 October 2024
- ...t1=L. A.|last1=Steen|first2=J. A.|last2=Seebach|title=[[Counterexamples in Topology]]|publisher=Dover|year=1995|pages=96–97|isbn=0-486-68735-X}}</ref> The set ...t1=L. A.|last1=Steen|first2=J. A.|last2=Seebach|title=[[Counterexamples in Topology]]|publisher=Dover|year=1995|page=3|isbn=0-486-68735-X}}</ref> ...3 KB (491 words) - 04:58, 6 February 2025
Page text matches
- ...topology]], the '''mapping spectrum''' <math>F(X, Y)</math> of [[spectrum (topology)|spectra]] ''X'', ''Y'' is characterized by {{topology-stub}} ...387 bytes (53 words) - 19:53, 10 August 2019
- ...a branch of [[mathematics]], a '''connective spectrum''' is a [[spectrum (topology)|spectrum]] whose [[homotopy]] sets <math>\pi_k</math> of negative degrees [[Category:Algebraic topology]] ...760 bytes (95 words) - 19:29, 26 March 2024
- {{short description|Mathematical theory related to general topology}} ...ional sequence topology''' is an example of a [[Topological space#topology|topology]] given to the set '''R''' of [[real number]]s. ...1,018 bytes (149 words) - 00:10, 5 June 2023
- ...oc=Ch 10. Section 7.}}</ref> Note ''B'' is not required to be a [[Subspace topology|subspace]] of ''A''. ...ite book | last=May | first=J. Peter | title=A concise course in algebraic topology | year=2019 | isbn=978-7-5192-6659-2 | oclc=1200780491}} ...803 bytes (113 words) - 16:03, 15 February 2022
- {{short description|Theorem in algebraic topology about the complex K-theory spectrum}} ...uced by [[Victor Snaith]], identifies the [[complex K-theory]] [[spectrum (topology)|spectrum]] with the [[localization of a spectrum|localization]] of the sus ...782 bytes (99 words) - 19:00, 27 July 2020
- ...t]] <math>\operatorname{SP}^\infty(X)</math> of a space ''X'' in algebraic topology ...452 bytes (59 words) - 21:18, 28 March 2018
- {{Distinguish|Overlapping interval topology}} ...topology]], the '''interlocking interval topology''' is an example of a [[topology]] on the set {{nowrap|1=''S'' := '''R'''<sup>+</sup> \ '''Z'''<sup>+</sup>} ...1 KB (193 words) - 01:54, 7 July 2024
- ...name{Spec}(A)</math> is a [[closed map]] with respect to the constructible topology. ...ral, the constructible topology is a [[finer topology]] than the [[Zariski topology]], and the two topologies coincide if and only if <math>A / \operatorname{n ...2 KB (316 words) - 23:51, 12 August 2023
- In algebraic topology, the '''Bousfield class''' of, say, a [[spectrum (topology)|spectrum]] ''X'' is the set of all (say) spectra ''Y'' whose [[smash produ {{topology-stub}} ...986 bytes (137 words) - 20:47, 28 January 2023
- ...tra point, say 0*, added. In this case, the double origin topology gives a topology on the set {{nowrap|1=''X'' = '''R'''<sup>2</sup> ∐ {0*} }}, where ∐ denote ...1995|isbn=0-486-68735-X}}</ref> We define a [[countably infinite]] [[Base (topology)|basis]] of neighbourhoods about the point 0 and about the additional point ...2 KB (322 words) - 08:55, 19 January 2022
- ...ogy''' is a certain [[Grothendieck topology]], which is finer than [[étale topology]]. Its main use is to define the cohomology of an [[algebraic stack]] with ...he cohomology of <math>B\mathbb{G}_m</math> should be defined using smooth topology for formulae like [[Behrend's fixed point formula]] to hold. ...1 KB (194 words) - 07:11, 26 June 2024
- ...rst=L. A.|last=Steen|first2=J. A.|last2=Seebach|title=[[Counterexamples in Topology]]|publisher=Dover|year=1995|page=140|ISBN=0-486-68735-X}}</ref> == Definition of the integer broom topology == ...3 KB (382 words) - 20:22, 7 February 2023
- ...of [[topology]], a '''free loop''' is a variant of the notion of a [[loop (topology)|loop]]. Whereas a loop has a distinguished point on it, called its basepo ...ce of all free loops <math>LX</math> has grown with the advent of [[string topology]], i.e. the study of new [[algebraic structure]]s on the [[singular homolog ...2 KB (263 words) - 22:38, 9 March 2024
- ...]] of [[homotopy]] classes of based maps from the [[Moore space (algebraic topology)|Moore space]] of type <math>(G, i)</math> to ''X'', and is denoted by <mat [[Category:Algebraic topology]] ...976 bytes (142 words) - 20:20, 20 December 2023
- {{distinguish|Linear bus topology}} ...ogical module|topological <math>A</math>-module]] with respect to a linear topology. ...2 KB (345 words) - 11:49, 28 November 2024
- ...f theorem''' (named after [[Heinz Hopf]]) is a statement in [[differential topology]], saying that the [[degree of a continuous mapping|topological degree]] is * {{cite book|last=Milnor|first= John W.|authorlink=John Milnor|title=Topology from the Differentiable Viewpoint|publisher=[[Princeton University Press]]| ...967 bytes (135 words) - 18:44, 10 October 2020
- ...plex]] <math>K</math>, the space <math>K\times [0,1]</math> is [[Collapse (topology)|collapsible]]. It can nowadays be restated as the claim that for any 2-com *{{citation|title=Algorithmic Topology and Classification of 3-Manifolds|volume=9|series=Algorithms and Computatio ...1 KB (154 words) - 18:31, 23 February 2025
- {{Short description|Concept in topology}} In mathematics, especially in algebraic topology, the '''mapping space''' between two spaces is the space of all the (contin ...2 KB (278 words) - 03:08, 27 January 2025
- {{short description|Topology in mathematics}} [[Category:Differential topology]] ...859 bytes (121 words) - 03:13, 28 September 2024
- ...t1=L. A.|last1=Steen|first2=J. A.|last2=Seebach|title=[[Counterexamples in Topology]]|publisher=Dover|year=1995|pages=96–97|isbn=0-486-68735-X}}</ref> The set ...t1=L. A.|last1=Steen|first2=J. A.|last2=Seebach|title=[[Counterexamples in Topology]]|publisher=Dover|year=1995|page=3|isbn=0-486-68735-X}}</ref> ...3 KB (491 words) - 04:58, 6 February 2025