Year: 2026
Type: preprint
Abstract: Let $A(X)$ denote the free Abelian topological group over a Tychonoff space $X$. We prove that if $A(X)$ and $A(Y)$ are topologically isomorphic and $X$ is countably compact, then $Y$ is also countably compact. Thus countable compactness is an $A$-invariant and, consequently, an $M$-invariant; this answers Open Problem~7.10.1 of Arhangel'skii and Tkachenko.
Source: arXiv (Cornell University)
Author: Huang, ZhouXiang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221165673