Topological Properties of the Space of Convex Minimal Usco Maps

Ľubica Holá; Branislav Novotný

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arXiv · 1803.01332

Topological Properties of the Space of Convex Minimal Usco Maps

Ľubica Holá·Branislav Novotný

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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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BibTeX RIS

Ľubica Holá, Branislav Novotný. 2018-03-04. Topological Properties of the Space of Convex Minimal Usco Maps. https://arxiv.org/abs/1803.01332

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