On a generalization of Hausdorff space.
Dutta, Tapas (1986)
International Journal of Mathematics and Mathematical Sciences
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Dutta, Tapas (1986)
International Journal of Mathematics and Mathematical Sciences
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Aleksander V. Arhangel'skii (2000)
Commentationes Mathematicae Universitatis Carolinae
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We show that there exists an Abelian topological group such that the operations in cannot be extended to the Dieudonné completion of the space in such a way that becomes a topological subgroup of the topological group . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions...
Constancio Hernández (2001)
Commentationes Mathematicae Universitatis Carolinae
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Let be a Tychonoff (regular) paratopological group or algebra over a field or ring or a topological semigroup. If and , then there exists a Tychonoff (regular) topology such that and is a paratopological group, algebra over or a topological semigroup respectively.
Oleg Okunev (1996)
Commentationes Mathematicae Universitatis Carolinae
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We observe the existence of a -compact, separable topological group and a countable topological group such that the tightness of is countable, but the tightness of is equal to .
(2012)
Fundamenta Mathematicae
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We investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has -diagonal. This implies, in particular, that every countably compact subspace of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary...