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...atowski's result allows them to be non-compact, but insists that their non-compactness "tends to zero" in an appropriate sense. The theorem is named for the [[Po ... ''X'', its [[measure of non-compactness|'''Kuratowski measure of non-compactness''']] ''α''(''A'') ≥ 0 is defined by ...

...heorem''', named after [[Jon Barwise]], is a generalization of the usual [[compactness theorem]] for [[first-order logic]] to a certain class of [[infinitary lang ...#5 "Infinitary Logic", Section 5, "Sublanguages of L(ω1,ω) and the Barwise Compactness Theorem"] ...

...d by Teck-Cheong Lim,<ref name="Lim">T.C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. '''60''' (1976), 179–182.</ref> and, soon after, un == Delta-compactness theorem == ...

...er to two theorems relating the closed [[convex hull]] and [[Compact space|compactness]] in the [[weak topology]]. They are named after [[Mark Krein]] and [[Vitol Both of the following theorems are referred to as the Krein-Smulian Theorem. ...

{{math theorem|name=James compactness criterion|note=|style=|math_statement= ...weak compactness of the unit sphere, Victor L. Klee reformulated this as a compactness criterion for the unit sphere in 1962 and assumes that this criterion chara ...

...h>T</math> ranges over the subset. From the [[finite intersection property|compactness]] of <math>K</math> it follows that the set *{{citation|first=S.|last=Kakutani|title=Two fixed point theorems concerning bicompact convex sets|year=1938|volume=14|pages=242–245|journal= ...

...compact. When restricted to a metric space ω-boundedness is equivalent to compactness. [[Category:Theorems in topology]] ...

{{Short description|Measure theory theorems}} ...l motivation for these theorems is fair division, they are in fact general theorems in [[measure theory]]. ...

...cite journal |last1= Sudakov |first1= V. N.|date= 1957 |title= Criteria of compactness in function spaces|language= Russian|journal= Upsekhi Math. Nauk. |volume=1 [[Category:Theorems in functional analysis]] ...

...inclusion]] for non-uniform upper [[hemicontinuity]] [[convex set]] with [[compactness]] in [[fuzzy set]].{{r|routledge|11th-national|dongqiu}} |title = Basic theorems for fuzzy differential equations in the quotient space of fuzzy numbers ...

...ncaré]], in 1895, and it extends the original [[Heine–Borel theorem]] on [[compactness]] for arbitrary [[Cover (topology)|covers]] of [[compact space|compact]] su ...tudied in [[reverse mathematics]] where it is one of the first third-order theorems that is hard to prove in terms of the comprehension axioms needed. ...

...t as their points, so compactness follows from [[Tychonoff's theorem]]. By compactness, every open cover has a finite subcover. The finite set of positions appear ...onfiguration of the automaton has exactly one predecessor. It follows by a compactness argument that the function mapping each configuration to its predecessor is ...

'''Cantor's intersection theorem''' refers to two closely related theorems in [[general topology]] and [[real analysis]], named after [[Georg Cantor]] [[Category:Compactness theorems]] ...

...N \right \}</math> is polyadic and compact directly from the definition of compactness, without using Heine-Borel. === Compactness === ...

...certain basic [[selection principle]] that generalizes [[Σ-compact space|σ-compactness]]. A Hurewicz space is a space in which for every sequence of open covers < ...e class of metric spaces his property is equivalent to <math>\sigma</math>-compactness. ...

...certain basic [[selection principle]] that generalizes [[σ-compact space|σ-compactness]]. A Menger space is a space in which for every sequence of open covers <ma title=Über eine verallgemeinerung des Borelschen Theorems| ...

...kicite|ref={{sfnRef|Lions|1985}}|reference=P.L. Lions. ''The concentration-compactness principle in the calculus of variations. The limit case. I.'' Rev. Mat. Ibe *{{wikicite|ref={{sfnRef|Willem|1996}}|reference=Michel Willem. ''Minimax theorems.'' Progress in Nonlinear Differential Equations and their Applications, 24. ...

...aphs in which every finite subgraph is planar (proved directly via Gödel's compactness theorem), see {{harvtxt|Rautenberg|2010}}.</ref> ...family of [[closed set]]s with the [[finite intersection property]], so by compactness it has a nonempty intersection. Every member of this intersection is a vali ...

[[Category:Theorems in functional analysis]] [[Category:Compactness theorems]] ...

| title = Compactness results in extremal graph theory [[Category:Theorems in graph theory]] ...