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 X contains, as a closed subspace, a homeomorphic copy of the product space X n {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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