On free topological algebras
Hans-E. Porst (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Hans-E. Porst (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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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.
R. Z. Buzyakova, A. Chigogidze (2011)
Fundamenta Mathematicae
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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples
Hentzel, I.R., Peresi, L.A. (2006)
Experimental Mathematics
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A. J. Kfoury (1988)
Banach Center Publications
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Caro, Yair (1990)
International Journal of Mathematics and Mathematical Sciences
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Jean Berstel (1985)
Publications du Département de mathématiques (Lyon)
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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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Jan Mycielski (1958)
Fundamenta Mathematicae
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Hans-E. Porst (1988)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Tomasz Schoen (2001)
Acta Arithmetica
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Sidney A. Morris (1976)
Colloquium Mathematicae
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Karl Dilcher, Lutz G. Lucht (2006)
Acta Arithmetica
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A. Kumar, P. K. Pathak (1976)
Colloquium Mathematicae
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