About: Hemicontinuity

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In mathematics, the notion of the continuity of functions is not immediately extensible to multivalued mappings or correspondences between two sets A and B. The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension. A correspondence that has both properties is said to be continuous in an analogy to the property of the same name for functions.

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rdfs:label	Hémicontinuité (fr) Hemicontinuity (en)
rdfs:comment	En mathématiques, les deux concepts topologiques duaux d'hémicontinuité supérieure et d'hémicontinuité inférieure permettent d'étendre aux multifonctions la notion de continuité d'une fonction. En analyse fonctionnelle un autre type d'hémicontinuité est défini pour les opérateurs d'un espace de Banach dans son dual topologique et en particulier pour les opérateurs d'un espace de Hilbert dans lui-même. (fr) In mathematics, the notion of the continuity of functions is not immediately extensible to multivalued mappings or correspondences between two sets A and B. The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension. A correspondence that has both properties is said to be continuous in an analogy to the property of the same name for functions. (en)
foaf:depiction
dcterms:subject	Variational analysis Mathematical analysis Continuous mappings
Wikipage page ID	2945778 (xsd:integer)
Wikipage revision ID	1119690979 (xsd:integer)
Link from a Wikipage to another Wikipage	Power set Uniform space Vietoris topology Continuous function Mathematics Function (mathematics) Choice function Function space Michael selection theorem Variational analysis Mathematical analysis Continuous mappings Hyperspace (topology) Multivalued function
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=KGtegVXqD8wC&pg=PA949 https://books.google.com/books%3Fid=cVUl3smcGlcC https://books.google.com/books%3Fid=ejhT-QMEVZ0C https://books.google.com/books%3Fid=rVnsCAAAQBAJ
sameAs	Hemicontinuity Hemicontinuity Hemicontinuity Hemicontinuity Hemicontinuity
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thumbnail	wiki-commons:Special:FilePath/Upper_hemicontinuous.svg?width=300
has abstract	In mathematics, the notion of the continuity of functions is not immediately extensible to multivalued mappings or correspondences between two sets A and B. The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension. A correspondence that has both properties is said to be continuous in an analogy to the property of the same name for functions. Roughly speaking, a function is upper hemicontinuous if when (1) a convergent sequence of points in the domain maps to a sequence of sets in the range which (2) contain another convergent sequence, then the image of the limiting point in the domain must contain the limit of the sequence in the range. Lower hemicontinuity essentially reverses this, saying if a sequence in the domain converges, given a point in the range of the limit, then you can find a sub-sequence whose image contains a convergent sequence to the given point. (en) En mathématiques, les deux concepts topologiques duaux d'hémicontinuité supérieure et d'hémicontinuité inférieure permettent d'étendre aux multifonctions la notion de continuité d'une fonction. En analyse fonctionnelle un autre type d'hémicontinuité est défini pour les opérateurs d'un espace de Banach dans son dual topologique et en particulier pour les opérateurs d'un espace de Hilbert dans lui-même. (fr)
prov:wasDerivedFrom	wikipedia-en:Hemicontinuity?oldid=1119690979&ns=0
page length (characters) of wiki page	9809 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hemicontinuity
is Link from a Wikipage to another Wikipage of	Nash equilibrium Upper hemicontinuity Upper hemicontinuous Kuratowski convergence Lower hemicontinuity Lower hemicontinuous Choice function Maximum theorem Michael selection theorem Fuzzy differential equation Hausdorff distance Kakutani fixed-point theorem Hemicontinuous Hemi-continuity Arrow–Debreu model Multivalued function Wijsman convergence Selection theorem Hemi-continuous Hemi Continuity Hemi continuity
is Wikipage redirect of	Upper hemicontinuity Upper hemicontinuous Lower hemicontinuity Lower hemicontinuous Hemicontinuous Hemi-continuity Hemi-continuous Hemi Continuity Hemi continuity
is foaf:primaryTopic of	wikipedia-en:Hemicontinuity

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