AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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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...
Abstract A topological group is called 𝑑-independent if, for every subgroup of cardinality less than the continuum, there exists a countable dense subgroup intersecting it trivially. This notion was introduced by Márquez and Tkachenko, who characterized 𝑑-independent second-countable locally compact abelian groups in p...
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