Extension of Borel maps with values in non-metrizable spaces

TL;DR

This paper explores conditions under which Borel and Baire-one maps with values in non-metrizable spaces can be extended from subspaces, focusing on spaces covered by sequences of metrizable spaces with specific properties.

Contribution

It introduces new criteria for extending Borel and Baire-one maps into non-metrizable target spaces covered by metrizable subspaces.

Findings

Established extension conditions for Borel maps in non-metrizable spaces.

Identified classes of non-metrizable spaces where extensions are possible.

Provided examples illustrating the extension process.

Abstract

We investigate the possibility of extension of $F_\sigma$-measurable and Baire-one maps from subspaces of topological spaces when these maps take values in spaces which covers by a sequence of metrizable spaces with special properties