The variety of topological groups generated by the free topological group on [0,1]
Sidney A. Morris (1976)
Colloquium Mathematicae
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Sidney A. Morris (1976)
Colloquium Mathematicae
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Sidney A. Morris (1972)
Matematický časopis
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Hans-E. Porst (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Vladimir Pestov, Dmitri Shakhmatov (1998)
Colloquium Mathematicae
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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.
Edward T. Ordman (1974)
Colloquium Mathematicae
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Edward T. Ordman (1974)
Colloquium Mathematicae
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Zygmunt Saloni (1974)
Colloquium Mathematicae
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Jeremy Brazas (2014)
Fundamenta Mathematicae
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The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.
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