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.
@article{118478,
author = {Jan Baars},
title = {Equivalence of certain free topological groups},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {33},
year = {1992},
pages = {125-130},
zbl = {0759.54022},
mrnumber = {1173754},
language = {en},
url = {http://dml.mathdoc.fr/item/118478}
}
Baars, Jan. Equivalence of certain free topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 125-130. http://gdmltest.u-ga.fr/item/118478/
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