Mardesic factorization theorem for asymptotic dimension

TL;DR

This paper establishes a coarse analogue of the Mardesic factorization theorem, demonstrating that coarsely continuous maps can be factored through spaces with controlled asymptotic dimension and weight.

Contribution

It introduces a new factorization theorem in coarse geometry, extending classical dimension theory results to the asymptotic setting.

Findings

Factorization of coarsely continuous maps through spaces with bounded asymptotic dimension.

Control over the weight of the intermediate space in the factorization.

Extension of classical dimension theory to coarse geometry context.

Abstract

The main goal of this note is to prove a coarse analogue of Factorization Theorems in Dimension Theory: Let $f: X \rightarrow Y$ be a coarsely continuous map. Then $f$ factors through coarsely continuous maps $g : X \rightarrow Z$ and $h : Z \rightarrow Y$ with asymptotic dimension of $Z$ at most asymptotic dimension of $X$ and the weight of $Z$ at most the weight of $Y$.