Applications of the Stone-Čech compactification to free topological groups

Hardy, J. P. L.; Morris, Sidney A.; Thompson, H. B.

doi:10.1090/S0002-9939-1976-0424994-X

Applications of the Stone-Čech compactification to free topological groups
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by J. P. L. Hardy, Sidney A. Morris and H. B. Thompson PDF

Proc. Amer. Math. Soc. 55 (1976), 160-164 Request permission

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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