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Proceedings of the American Mathematical Society

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Applications of the Stone-Čech compactification to free topological groups


Authors: J. P. L. Hardy, Sidney A. Morris and H. B. Thompson
Journal: Proc. Amer. Math. Soc. 55 (1976), 160-164
MSC: Primary 22A05; Secondary 54D35
DOI: https://doi.org/10.1090/S0002-9939-1976-0424994-X
MathSciNet review: 0424994
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Abstract: In this note the Stone-Čech compactification is used to produce short proofs of two theorems on the structure of free topological groups. The first is: The free topological group on any Tychonoff space $ X$ contains, as a closed subspace, a homeomorphic copy of the product space $ {X^n}$. This is a generalization of a result of B. V. S. Thomas. The second theorem proved is C. Joiner's, Fundamental Lemma.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0424994-X
Keywords: Free topological group, Stone-Čech compactification, Tychonoff space
Article copyright: © Copyright 1976 American Mathematical Society