About: Michael selection theorem

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In functional analysis, a branch of mathematics, Michael selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following: Let X be a paracompact space and Y a Banach space.Let be a lower hemicontinuous multivalued map with nonempty convex closed values.Then there exists a continuous selection of F.Conversely, if any lower semicontinuous multimap from topological space X to a Banach space, with nonempty convex closed values, admits a continuous selection, then X is paracompact. This provides another characterization for paracompactness.

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rdfs:label	Théorème de sélection de Michael (fr) Michael selection theorem (en)
rdfs:comment	In functional analysis, a branch of mathematics, Michael selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following: Let X be a paracompact space and Y a Banach space.Let be a lower hemicontinuous multivalued map with nonempty convex closed values.Then there exists a continuous selection of F.Conversely, if any lower semicontinuous multimap from topological space X to a Banach space, with nonempty convex closed values, admits a continuous selection, then X is paracompact. This provides another characterization for paracompactness. (en) En mathématiques, le théorème de sélection de Michael, est un théorème d'analyse fonctionnelle démontré en 1956 par (en). Il s'énonce comme suit : Si X est un espace paracompact alors, toute multifonction hémicontinue inférieurement Γ, de X dans un espace de Banach E et à valeurs des convexes fermées non vides, possède une « sélection » continue, c'est-à-dire qu'il existe une application continue f : X → E telle que pour tout x de X, f(x) appartienne à Γ(x). Michael a aussi démontré la réciproque, si bien que cette propriété caractérise les espaces paracompacts (parmi les espaces séparés). (fr)
foaf:depiction
dcterms:subject	Theorems in functional analysis Properties of topological spaces Continuous mappings Compactness theorems
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Wikipage revision ID	1068328230 (xsd:integer)
Link from a Wikipage to another Wikipage	Convex set Theorems in functional analysis Properties of topological spaces Converse (logic) Lower hemicontinuous Lower semi-continuous Choice function Closed set Functional analysis Hemicontinuity Banach space Topological vector space Ernest Michael Paracompact space Differential inclusion Peano existence theorem Topology and its Applications Continuous mappings Compactness theorems Continuous function (topology) Paracompact Multivalued function Normed vector space Selection theorem dbr:Zero-dimensional_Michael_selection_theorem
sameAs	Michael selection theorem Michael selection theorem Michael selection theorem Michael selection theorem Michael selection theorem
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has abstract	In functional analysis, a branch of mathematics, Michael selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following: Let X be a paracompact space and Y a Banach space.Let be a lower hemicontinuous multivalued map with nonempty convex closed values.Then there exists a continuous selection of F.Conversely, if any lower semicontinuous multimap from topological space X to a Banach space, with nonempty convex closed values, admits a continuous selection, then X is paracompact. This provides another characterization for paracompactness. (en) En mathématiques, le théorème de sélection de Michael, est un théorème d'analyse fonctionnelle démontré en 1956 par (en). Il s'énonce comme suit : Si X est un espace paracompact alors, toute multifonction hémicontinue inférieurement Γ, de X dans un espace de Banach E et à valeurs des convexes fermées non vides, possède une « sélection » continue, c'est-à-dire qu'il existe une application continue f : X → E telle que pour tout x de X, f(x) appartienne à Γ(x). Michael a aussi démontré la réciproque, si bien que cette propriété caractérise les espaces paracompacts (parmi les espaces séparés). (fr)
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foaf:isPrimaryTopicOf	wikipedia-en:Michael_selection_theorem
is Link from a Wikipage to another Wikipage of	Hemicontinuity Ernest Michael Paracompact space Multivalued function Selection theorem Michael's continuous selection theorem
is Wikipage redirect of	Michael's continuous selection theorem
is foaf:primaryTopic of	wikipedia-en:Michael_selection_theorem

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