Lowering mean topological dimension

TL;DR

This paper proves that certain topological dynamical systems with positive mean topological dimension and marker property can be decomposed into factors with arbitrarily small or zero mean topological dimension, aiding in understanding their structure.

Contribution

It introduces a method to decompose systems with positive mean topological dimension into factors with smaller or zero mean dimension, expanding the understanding of their structure.

Findings

Existence of factors with arbitrarily small mean topological dimension

Existence of zero relative mean topological dimension factors

Separation of points by these factors

Abstract

In this paper, we prove that for a topological dynamical system with positive mean topological dimension and marker property, it has factors of arbitrary small mean topological dimension and zero relative mean topological dimension which separate points.