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Equivalence of certain free topological groups. (English) Zbl 0759.54022
In the earlier paper of the author and J. de Groot [Comment. Math. Univ. Carol. 29, 577-595 (1988; Zbl 0684.54011)], a complete linear homeomorphic classification of function spaces $$C_ p(X)$$ of locally compact zero-dimensional separable metric spaces $$X$$ was given. In the paper under review the author presents a clear proof that the above classification is completely analogous to an isomorphic classification of free topological groups $$FM(X)$$ of the same spaces $$X$$. This implies, in particular, that the groups $$FM(X)$$ and $$FM(Y)$$ are isomorphic for any uncountable zero-dimensional compact metric spaces $$X$$ and $$Y$$. The zero- dimensionality assumption is essential, because the free topological groups of the unit interval and the “letter” $$T$$ are not isomorphic by the well-known result of M. I. Graev.

##### MSC:
 54H11 Topological groups (topological aspects) 54C35 Function spaces in general topology 22A05 Structure of general topological groups
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