A relatively free topological group that is not varietal free
Volume 77 / 1998
Colloquium Mathematicum 77 (1998), 1-8
DOI: 10.4064/cm-77-1-1-8
Abstract
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.
