A relatively free topological group that is not varietal free

Volume 77 / 1998

Vladimir Pestov, Dmitri Shakhmatov Colloquium Mathematicum 77 (1998), 1-8 DOI: 10.4064/cm-77-1-1-8


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.


  • Vladimir Pestov
  • Dmitri Shakhmatov

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