Densely defined selections of multivalued mappings

Čoban, M. M.; Kenderov, P. S.; Revalski, J. P.

doi:10.1090/S0002-9947-1994-1154539-6

Densely defined selections of multivalued mappings
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by M. M. Čoban, P. S. Kenderov and J. P. Revalski PDF

Trans. Amer. Math. Soc. 344 (1994), 533-552 Request permission

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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