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In mathematics, the notion of the continui … 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. a convergent sequence to the given point.
, En mathématiques, les deux concepts topolo … 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.eurs d'un espace de Hilbert dans lui-même.
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In mathematics, the notion of the continui … 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.e property of the same name for functions.
, En mathématiques, les deux concepts topolo … 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.eurs d'un espace de Hilbert dans lui-même.
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Hemicontinuity
, Hémicontinuité
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