Geodesic
Equivalence of certain free topological groups
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 125-130

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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.
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.
Classification : 22A05, 54C35, 54H11
Keywords: free topological groups; function spaces 
Baars, Jan. Equivalence of certain free topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 125-130. http://geodesic.mathdoc.fr/item/CMUC_1992_33_1_a14/
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