Point-finite collection
Dieudonné's theorem: lk
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{{math_theorem|math_statement={{Citation | last1=Dieudonné | first1=Jean | author1-link=Jean Dieudonné | title=Une généralisation des espaces compacts | mr=0013297 | year=1944 | journal=[[Journal de Mathématiques Pures et Appliquées]]|series= Neuvième Série | issn=0021-7824 | volume=23 | pages=65–76}}, Théorème 6.{{sfn|Willard|2012|loc=Theorem 15.10}} A topological space is [[normal space|normal]] if and only if each point-finite open cover of has a [[shrinking (topology)|shrinking]]; that is, if is an open cover indexed by a set , there is an open cover indexed by the same set such that for each .}} |
{{math_theorem|math_statement={{Citation | last1=Dieudonné | first1=Jean | author1-link=Jean Dieudonné | title=Une généralisation des espaces compacts | mr=0013297 | year=1944 | journal=[[Journal de Mathématiques Pures et Appliquées]]|series= Neuvième Série | issn=0021-7824 | volume=23 | pages=65–76}}, Théorème 6.{{sfn|Willard|2012|loc=Theorem 15.10}} A topological space is [[normal space|normal]] if and only if each point-finite open cover of has a [[shrinking (topology)|shrinking]]; that is, if is an open cover indexed by a set , there is an open cover indexed by the same set such that for each .}} |
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The original proof uses Zorn's lemma, while Willard uses transfinite recursion. |
The original proof uses [[Zorn's lemma]], while Willard uses [[transfinite recursion]]. |
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==References== |
==References== |
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