Mean topological dimension of induced amenable group actions

TL;DR

This paper extends the concept of mean topological dimension from single transformations to actions of amenable groups, providing a positive answer to an open question in the field.

Contribution

It generalizes previous results on mean topological dimension to the setting of amenable group actions, addressing an open problem.

Findings

Extended mean topological dimension to amenable group actions

Provided an affirmative answer to an open question in the literature

Generalized previous single transformation results to group actions

Abstract

In this paper we generalize [BS22, Main Theorem] from actions of a single transformation to amenable group actions, which answers affirmatively the question raised in [BS22] by Burguet and the first-named author of the paper.