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Local Compactness In Free Topological Groups, Peter Nickolas, Mikhail Tkachenko

Faculty of Engineering and Information Sciences - Papers: Part A

We show that the subspace A_n(X) of the free Abelian topological group A(X) on a Tychonoff space X is locally compact for each n ω if and only if A₂(X) is locally compact if an only if F₂(X) is locally compact if and only if X is the topological sum of a compact space and a discrete space. It is also proved that the subspace F_n(X) of the free topological group F(X) is locally compact for each n …