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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Free topological groups and dimension

Author: Charles Joiner
Journal: Trans. Amer. Math. Soc. 220 (1976), 401-418
MSC: Primary 22A05; Secondary 54F45
MathSciNet review: 0412322
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Abstract: For a completely regular space X we denote by $ F(X)$ and $ A(X)$ the free topological group of X and the free Abelian topological group of X, respectively, in the sense of Markov and Graev.

Let X and Y be locally compact metric spaces with either $ A(X)$ topologically isomorphic to $ A(Y)$ or $ F(X)$ topologically isomorphic to $ F(Y)$. We show that in either case X and Y have the same weak inductive dimension. To prove these results we use a Fundamental Lemma which deals with the structure of the topology of $ F(X)$ and $ A(X)$. We give other results on the topology of $ F(X)$ and $ A(X)$ and on the position of X in $ F(X)$ and $ A(X)$.

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Keywords: Free topological group, free Abelian topological group, dimension, compactness, paracompactness, automorphism, varieties of topological groups
Article copyright: © Copyright 1976 American Mathematical Society

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