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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Edward T. Ordman (1974)
Colloquium Mathematicae
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Edward T. Ordman (1974)
Colloquium Mathematicae
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Hans-E. Porst (1988)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Sidney A. Morris (1974)
Matematický časopis
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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.
L. Außenhofer, M. J. Chasco, X. Domínguez, V. Tarieladze (2007)
Studia Mathematica
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We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact k-spaces are Schwartz groups. We also prove that every hemicompact k-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group. ...
Hans-E. Porst (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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