Linear operators with compact supports, probability measures and Milyutin maps

TL;DR

This paper introduces regular operators with compact supports, characterizes absolute extensors for zero-dimensional spaces, and explores how Milyutin maps preserve key topological properties.

Contribution

It defines regular operators with compact supports and links them to absolute extensors, also analyzing the preservation of topological properties under Milyutin maps.

Findings

Characterization of absolute extensors for zero-dimensional spaces.

Milyutin maps preserve paracompactness, metrizability, and k-metrizability.

Abstract

The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and k-metrizability, are preserved under Milyutin maps.