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Applications of the Stone-Čech Compactification to Free Topological Groups

J. P. L. Hardy, Sidney A. Morris and H. B. Thompson
Proceedings of the American Mathematical Society
Vol. 55, No. 1 (Feb., 1976), pp. 160-164
DOI: 10.2307/2041864
Stable URL: http://www.jstor.org/stable/2041864
Page Count: 5
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Applications of the Stone-Čech Compactification to Free Topological Groups
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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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