About extension of upper semicontinuous multi-valued maps and applications (Q2786106)

The following theorem is the main result of the paper: Let \(X\) be a separated topological space, \(A\) be a closed subset of \(X\), and \(T:A\to [0,1]\) be a \(usc\) multi-valued map with closed convex values. Suppose that either \(X\) is completely normal, or \(X\) is normal and \(A\) is perfectly normal. Then \(T\) can be extended to a \(usc\) multi-valued map with closed convex values defined on whole \(X\) into \([0,1]\). In the second part of the paper some applications of this theorem to theory of fixed points of multifunctions and to qualitative games are given.