Applications of the Stone-Cech Compactification to Free Topological Groups

Abstract

In this note the Stone-Cech 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. This is a generalization of a result of B. V. S. Thomas. The second theorem proved is C. Joiner’s, Fundamental Lemma.