Densely defined selections of multivalued mappings
Mustafa Çoban, Petar S. Kenderov, J. P. Revalski · Transactions of the American Mathematical Society · 1994
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.