upper semicontinuity

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Hemicontinuity — In mathematics, the concept of continuity as it is defined for single valued functions is not immediately extendible to multi valued mappings or correspondences. In order to derive a more generalized definition, the dual concepts of upper… … Wikipedia
Kakutani fixed point theorem — In mathematical analysis, the Kakutani fixed point theorem is a fixed point theorem for set valued functions. It provides sufficient conditions for a set valued function defined on a convex, compact subset of a Euclidean space to have a fixed… … Wikipedia
Semi-continuity — For the notion of upper or lower semicontinuous multivalued function see: Hemicontinuity In mathematical analysis, semi continuity (or semicontinuity) is a property of extended real valued functions that is weaker than continuity. A extended real … Wikipedia
semicontinuous — adjective (of a function) That it is continuous almost everywhere, except at certain points at which it is either upper semi continuous or lower semi continuous. See Also: semicontinuity, hemicontinuous … Wiktionary

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