Selections for Paraconvex-valued Mappings on Non-paracompact Domains

TL;DR

This paper extends Michael's selection theorem for paraconvex-valued mappings from paracompact spaces to collectionwise normal spaces, broadening the theorem's applicability.

Contribution

It demonstrates that the paraconvex-valued selection theorem holds on collectionwise normal spaces, not just paracompact spaces, and discusses potential generalizations.

Findings

The theorem applies to C'(E)-valued mappings on collectionwise normal spaces.

The extension broadens the class of spaces where the selection theorem is valid.

Possible generalizations of the theorem are proposed.

Abstract

We prove that Michael's paraconvex-valued selection theorem for paracompact spaces remains true for C'(E)-valued mappings defined on collectionwise normal spaces. Some possible generalisations are also given.