Geodesic
A relatively free topological group that is not varietal free
Colloquium Mathematicum, Tome 77 (1998) no. 1, pp. 1-8.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-77-1-1-8
Keywords: relatively free topological group, variety of topological groups, free zero-dimensional topological group, varietal free topological group

Vladimir Pestov 1 ; Dmitri Shakhmatov 1

1 
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Vladimir Pestov; Dmitri Shakhmatov. A relatively free topological group that is not varietal free. Colloquium Mathematicum, Tome 77 (1998) no. 1, pp. 1-8. doi : 10.4064/cm-77-1-1-8. http://geodesic.mathdoc.fr/articles/10.4064/cm-77-1-1-8/

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