Topological Properties of the Space of Convex Minimal Usco Maps

2018/03/04 by Holá, Ľubica, Novotný, Branislav
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1803.01332

Abstract

Let X be a Tychonoff space and MC(X) be the space of convex minimal usco maps with values in R, the space of real numbers. Such set-valued maps are important in the study of subdifferentials of convex functions. Using the strong Choquet game we prove complete metrizability of MC(X) with the upper Vietoris topology. If X is normal, elements of MC(X) can be approximated in the Vietoris topology by continuous functions. We also study first countability, second countability and other properties of the upper Vietoris topology on MC(X).

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