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

Abstract

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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.

How to cite

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Pestov, 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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  21. [21] D. B. Shakhmatov, Imbeddings into topological groups preserving dimensions, Topology Appl. 36 (1990), 181-204. Zbl0709.22001

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