Hartman-Mycielski functor of non-metrizable compacta

TL;DR

This paper studies a specific topological functor related to the Hartman-Mycielski construction, analyzing its properties such as openness and conditions for being an absolute retract, especially in non-metrizable compact spaces.

Contribution

It introduces new topological properties of Radul's functor, including criteria for when it produces absolute retracts homeomorphic to Tychonov cubes.

Findings

The functor H is open.

Conditions identified for HX to be an absolute retract.

HX can be homeomorphic to the Tychonov cube under certain conditions.

Abstract

We investigate some topological properties of a normal functor $H$ introduced earlier by Radul which is a certain functorial compactification of the Hartman-Mycielski construction $HM$. We show that $H$ is open and find the condition when $HX$ is an absolute retract homeomorphic to the Tychonov cube.