Displaying similar documents to “Local compactness and local invariance of free products of topological groups”

A relatively free topological group that is not varietal free

Vladimir Pestov, Dmitri Shakhmatov (1998)

Colloquium Mathematicae

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Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.