Michael selection problem in hyperconvex metric spaces (Q1431136)

The Michael selection problem asks: If \(X\) is a paracompact topological space and \(F:X\to 2^{Y}\) is lower semicontinuous with nonempty closed convex values, does the Michael selection theorem hold if \(Y\) is a non-locally convex convex complete metrizable topological linear space? In the present paper, a positive answer is given for the case of a sub-admissible subset of a hyperconvex metric space. As a consequence, a fixed point theorem is also given.