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{{short description|Establishes the concept of stabilization of homotopy groups}} {{redirect|Suspension theorem|the theorem in homology|Excision theorem#Suspension theorem for homology}} ...

...ption|When a mapping that induces isomorphisms on all homotopy groups is a homotopy equivalence}} ...gy]], in which the behavior of certain algebraic invariants (in this case, homotopy groups) determines a topological property of a mapping. ...

In [[mathematics]], the '''Andreotti–Frankel theorem''', introduced by {{harvs ...]] with critical points of index at most ''n'', and so <math>V</math> is [[homotopy equivalent]] to a [[CW complex]] of [[real dimension]] at most ''n''. ...

{{short description|Gives a homomorphism from homotopy groups to homology groups}} ...of [[algebraic topology]], connecting [[homotopy theory]] with [[homology theory]] via a map known as the '''Hurewicz homomorphism'''. The theorem is named ...

In [[mathematics]], the '''universal bundle''' in the theory of [[fiber bundle]]s with structure group a given [[topological group]] {{m ===In the CW complex category=== ...

{{short description|Theorem in homotopy theory}} ...'. The conjecture was made in the mid 1970s by [[Graeme Segal]] and proved in 1984 by [[Gunnar Carlsson]]. This statement is still commonly referred to a ...

...of mathematical research with its origins in [[topological]] [[fixed-point theory]]. Its central ideas were developed by Danish mathematician [[Jakob Nielsen The theory developed in the study of the so-called ''minimal number'' of a [[map (mathematics)|map] ...

...and sufficient condition]]s for a [[contravariant functor]] ''F'' on the [[homotopy category]] ''Hotc'' of pointed connected [[CW complex]]es, to the [[categor ...theorem is often stated for functors to the category of [[pointed set]]s; in other words the sets are also given a base point. ...

{{Short description|Concept in math}} ...s two [[topological space|spaces]] that have the same shape. The phrase is in fact used for two different (but related) categories, as discussed below. ...

In [[mathematics]], specifically [[algebraic topology]], the '''mapping cylind :<math>(0,x)\sim f(x)\quad\text{for each }x\in X.</math> ...

...sizes of the “holes” in ''X''. This condition is necessary for most of the theory of covering spaces, including the existence of a [[universal cover]] and th ...The neighborhood ''U'' need not be [[simply connected]]: though every loop in ''U'' must be contractible within ''X'', the contraction is not required to ...

In [[mathematics]], '''Kuiper's theorem''' (after [[Nicolaas Kuiper]]) is a re ...py group]]s are trivial. This result has important uses in [[topological K-theory]]. ...

...ion]]s, and the phrase '''Milnor fibration''' is more commonly encountered in the mathematical literature. These were introduced to study isolated singul ...the original motivations for studying such maps was in the study of [[Knot theory|knots]] constructed by taking an <math>\varepsilon</math>-ball around a sin ...

{{short description|Describes a periodicity in the homotopy groups of classical groups}} ...heory associated to the [[unitary group]]. See for example [[topological K-theory]]. ...

...date=March 2019}}. '''Calculus of fractions''' is another name for working in a localized category. ...y situations, it is meaningful to replace ''C'' by another category ''C''' in which certain morphisms are forced to be isomorphisms. This process is call ...

.... [[Duality (category theory)|Dually]], a '''cocomplete category''' is one in which all small [[colimit]]s exist. A '''bicomplete category''' is a catego ==Theorems== ...

...that are preserved under [[Continuous function|continuous]] [[Deformation theory|deformations]], such as [[Stretch factor|stretching]], [[Twist (differentia ...deformations that are considered in topology are [[homeomorphism]]s and [[homotopy|homotopies]]. A property that is invariant under such deformations is a [[t ...

{{See also|List of examples in general topology}} *[[Metrization theorems]] ...

...tional language for mathematics]]<br />[[Modal logic|Modal]] homotopy type theory ...mathematics]] and [[philosophy of psychology]]. He was [[Senior Lecturer]] in Philosophy at the [[University of Kent]] until 2024. ...

In [[mathematics]], the '''simplicial approximation theorem''' is a foundation ...n general compatible with the [[pathological (mathematics)|pathological]], in some other areas. This initiated, one could say, the era of [[combinatorial ...