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{{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 ...

...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]]| ...

{{short description|Offers a substitute for the absence of excision in homotopy theory}} ...em''' offers a substitute for the absence of [[Excision theorem|excision]] in [[homotopy theory]]. More precisely, let <math>(X; A, B)</math> be an [[exc ...

...|mr=2009|pages=556–583|series=Second Series|title=On regularly convex sets in the space conjugate to a Banach space|volume=41|year=1940|issue=3 |jstor=19 Both of the following theorems are referred to as the Krein-Smulian Theorem. ...

The '''Mackey–Arens theorem''' is an important theorem in [[functional analysis]] that characterizes those [[locally convex]] [[Topol {{Main|Polar topology|Mackey topology}} ...

{{Short description|Two theorems needed for Quillen's Q-construction in algebraic K-theory}} ...ian]]. The two theorems play central roles in Quillen's [[Q-construction]] in [[algebraic K-theory]] and are named after [[Daniel Quillen]]. ...

In [[mathematics]], the '''bagpipe theorem''' of {{harvs|txt|last=Nyikos|first .... For example, the [[long line (topology)|long line]] and the [[long line (topology)|closed long ray]] are ω-bounded but not compact. When restricted to a metr ...

...implicit in the use of [[piecewise function]]s. For example, in the book ''Topology and Groupoids'', where the condition given for the statement below is that ...roupoid]] of a [[topological space]]; it allows one to concatenate [[path (topology)|path]]s to create a new path. ...

In [[general topology]], a '''remote point''' is a [[Point (geometry)|point]] <math>p</math> that Let <math>\R</math> be the [[real line]] with the standard topology. In 1962, [[Nathan Fine]] and [[Leonard Gillman]] proved that, assuming the [[c ...

...certain [[metric space]]s, named after [[Wacław Sierpiński]] who proved it in 1920.{{r|sierpiński}} ...point]]s is [[homeomorphic]] to <math>\mathbb{Q}</math> (with its standard topology).{{r|sierpiński|błaszczyk|dasgupta|engelking|kechris|van-mill}} ...

{{DISPLAYTITLE:Basic theorems in algebraic ''K''-theory}} {{short description|Four mathematical theorems}} ...

...matics)|knot]]s or [[link (knot theory)|link]]s. The conditions are stated in terms of the [[group (mathematics)|group]] structures on braids. ...ates that every [[knot (mathematics)|knot]] or [[link (knot theory)|link]] in three-dimensional Euclidean space is the closure of a [[braid (mathematics) ...

In [[mathematics]], at the intersection of [[algebraic topology]] and [[algebraic geometry]], there is the notion of a [[Hopf algebroid]] w == Structure theorems == ...

...owing that a distance-preserving map, which is a priori only [[continuity (topology)|continuous]], is actually [[Differentiable function|differentiable]]. ...row M</math> is <math display="inline">\mathcal{C}^1</math>differentiable (in both variables). This is a generalization of the easier, similar statement ...

In [[mathematics]], in the areas of [[topology]] and [[functional analysis]], the '''Anderson–Kadec theorem''' states<ref> .../math>'' of the dual space <math>X^*</math> if for each sequence <math>x_n\in X</math> the following condition is satisfied: ...

...s function|continuous]] at [[zero]] in the ''Sazonov topology'' and such a topology is called ''sufficient''. The theorem is named after the two [[Russia|Russi ...t |last=Schwartz |publisher=Tata Institute of Fundamental Research Studies in Mathematics |title=Radon measures on arbitrary topological spaces and cylin ...

{{Short description|Mathematical construction in topology}} ...atowski theorems|Borel space]] associated with a [[Polish space]]. Except in the case of [[discrete space|discrete]] Polish spaces, the standard Borel s ...

In [[mathematics]], '''Novikov's compact leaf theorem''', named after [[Sergei ...up> had a compact leaf, which was known to be true for all known examples; in particular, the [[Reeb foliation]] has a compact leaf that is&nbsp;''T''<su ...

{{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 ...

...[[Banach space]] into itself to have a fixed point. The result was proved in 1968 by Clifford Earle and [[Richard S. Hamilton]] by showing that, with re *the image ''f''(''D'') is bounded in norm; ...