Mardesic factorization theorem for asymptotic dimension

Abstract

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