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Michael selection theorem : ウィキペディア英語版
Michael selection theorem
In functional analysis, a branch of mathematics, the most popular version of the Michael selection theorem, named after Ernest Michael, states the following:
: Let ''E'' be a Banach space, ''X'' a paracompact space and φ : ''X'' → ''E'' a lower hemicontinuous multivalued map with nonempty convex closed values. Then there exists a continuous selection ''f'' : ''X'' → ''E'' of φ.
: Conversely, if any lower semicontinuous multimap from topological space ''X'' to a Banach space, with nonempty convex closed values admits continuous selection, then ''X'' is paracompact. This provides another characterization for paracompactness.
== See also ==

* Zero-dimensional Michael selection theorem
* List of selection theorems

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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