A characterization of Erdős space factors

Abstract

We prove that an almost zero-dimensional space $X$ is an Erdős space factor if and only if $X$ has a Sierpiński stratification of C-sets. We apply this characterization to spaces which are countable unions of C-set Erdős space factors. We show that the Erdős space $\mathfrak{E}$ is unstable by giving strongly $\sigma$-complete and nowhere $\sigma$-complete examples of almost zero-dimensional $F_{\sigma \delta }$-spaces which are not Erdős space factors. This answers a question by Dijkstra and van Mill.

8 pages

References in corpus (1)

• Symmetric products of Erdős space and complete Erdős space

Cited by in corpus (1)

• A characterization of the product of the rational numbers and complete Erdős space