Glasner's problem for Polish groups with metrizable universal minimal flow

TL;DR

This paper addresses Glasner's problem by showing that Polish groups with a metrizable universal minimal flow are extremely amenable, providing a positive answer under this additional assumption.

Contribution

It demonstrates that Glasner's problem has a positive solution for Polish groups with a metrizable universal minimal flow, advancing understanding in topological dynamics.

Findings

Polish groups with metrizable universal minimal flow are extremely amenable

Positive answer to Glasner's problem under the metrizability assumption

Highlights the significance of the universal minimal flow's topology

Abstract

A problem of Glasner, now known as Glasner's problem, asks whether every minimally almost periodic, monothetic, Polish groups is extremely amenable. The purpose of this short note is to observe that a positive answer is obtained under the additional assumption that the universal minimal flow is metrizable.