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Countable compactness is $A$-invariant
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
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