Properties of Sets Admitting Stable $\varepsilon$-Selectionsстатья
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Аннотация:Sets in which some convex subsets admit local (global) continuous $\varepsilon$-selections are studied. In particular, it is shown that if, for any number $\varepsilon>0$, some neighborhood O(x) of a point x in a Banach space X contains a dense (in O(x)) convex set K admitting an upper semicontinuous acyclic (in particular, continuous single-valued) $\varepsilon$-selection to an approximatively compact set M⊂X, then x is a $\delta$-sun point; if, in addition, X∈(R), then the set of all points nearest to x in M is a singleton.