Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1976-0412322-X
MathSciNet review: 0412322
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22A05, 54F45

Retrieve articles in all journals with MSC: 22A05, 54F45


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0412322-X
Keywords: Free topological group, free Abelian topological group, dimension, compactness, paracompactness, automorphism, varieties of topological groups
Article copyright: © Copyright 1976 American Mathematical Society