# A relatively free topological group that is not varietal free

Vladimir Pestov; Dmitri Shakhmatov

Colloquium Mathematicae (1998)

- Volume: 77, Issue: 1, page 1-8
- ISSN: 0010-1354

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topPestov, Vladimir, and Shakhmatov, Dmitri. "A relatively free topological group that is not varietal free." Colloquium Mathematicae 77.1 (1998): 1-8. <http://eudml.org/doc/210574>.

@article{Pestov1998,

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.},

author = {Pestov, Vladimir, Shakhmatov, Dmitri},

journal = {Colloquium Mathematicae},

keywords = {relatively free topological group; variety of topological groups; free zero-dimensional topological group; varietal free topological group; topological groups; variety; algebraically free},

language = {eng},

number = {1},

pages = {1-8},

title = {A relatively free topological group that is not varietal free},

url = {http://eudml.org/doc/210574},

volume = {77},

year = {1998},

}

TY - JOUR

AU - Pestov, Vladimir

AU - Shakhmatov, Dmitri

TI - A relatively free topological group that is not varietal free

JO - Colloquium Mathematicae

PY - 1998

VL - 77

IS - 1

SP - 1

EP - 8

AB - 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.

LA - eng

KW - relatively free topological group; variety of topological groups; free zero-dimensional topological group; varietal free topological group; topological groups; variety; algebraically free

UR - http://eudml.org/doc/210574

ER -

## References

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