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ArticleOriginal scientific text

Title

A relatively free topological group that is not varietal free

Authors 1, 2

Affiliations

  1. School of Mathematical and Computing Sciences, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand
  2. Department of Mathematical Sciences, Faculty of Science, Ehime University, Matsuyama 790, Japan

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.

Keywords

ENG
relatively free topological group, variety of topological groups, free zero-dimensional topological group, varietal free topological group

Bibliography

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Colloquium Mathematicum
1998/77/1
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Pages:
1-8
Main language of publication
English
Received
1997-04-24
Published
1998
Exact and natural sciences