Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Densely defined selections of multivalued mappings

Authors: M. M. Čoban, P. S. Kenderov and J. P. Revalski
Journal: Trans. Amer. Math. Soc. 344 (1994), 533-552
MSC: Primary 54C65; Secondary 46G99, 47H04, 49J40, 54C60
MathSciNet review: 1154539
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Abstract: Rather general suficient conditions are found for a given multivalued mapping $ F:X \to Y$ to possess an upper semicontinuous and compact-valued selection G which is defined on a dense $ {G_\delta }$-subset of the domain of F. The case when the selection G is single-valued (and continuous) is also investigated. The results are applied to prove some known as well as new results concerning generic differentiability of convex functions, Lavrentieff type theorem, generic well-posedness of optimization problems and generic non-multivaluedness of metric projections and antiprojections.

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Keywords: Multivalued mappings, selections, semicontinuity, generic continuity, Baire category
Article copyright: © Copyright 1994 American Mathematical Society