Jan Baars
Equivalence of certain free topological groups

Comment.Math.Univ.Carolinae 33,1 (1992) 125-130.

Abstract:In this paper we give a complete isomorphical classification of free topological groups $FM(X)$ of locally compact zero-dimensional separable metric spaces $X$. From this classification we obtain for locally compact zero-dimensional separable metric spaces $X$ and $Y$ that the free topological groups $FM (X)$ and $FM(Y)$ are isomorphic if and only if $C_p(X)$ and $C_p(Y)$ are linearly homeomorphic.

Keywords: free topological groups, function spaces
AMS Subject Classification: Primary 22A05; Secondary 54C35

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