Graph approximations of set-valued maps under constraints

Jarosław Mederski

Abstract


In the paper we study the existence of constrained graph approximations of
set-valued maps with non-convex values. We prove, in particular, that
any open neighbourhood of the graph of a map satisfying the so-called
topological tangency assumptions contains a graph of constrained continuous
single-valued map provided that the domain is finite-dimensional.

Keywords


Fiberwise retraction; fiberwise absolute neighbourhood extensor over B; locally n-connected space; set-valued map

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