Topologies in -groups
Bohumil Šmarda (1967)
Archivum Mathematicum
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Bohumil Šmarda (1967)
Archivum Mathematicum
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Aleksander V. Arhangel'skii, Miroslav Hušek (2001)
Commentationes Mathematicae Universitatis Carolinae
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The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group that is not Dieudonné complete one can find a Dieudonné complete group such that the Dieudonné completion of is not a topological group containing as a subgroup. Using Korovin’s construction of -dense orbits, we present some examples showing that some results on topological groups are not valid...
Nurettin Bağırmaz, İlhan İçen, Abdullah F. Özcan (2016)
Topological Algebra and its Applications
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The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.
Rangan, G. (1985)
International Journal of Mathematics and Mathematical Sciences
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Milnes, Paul (1994)
International Journal of Mathematics and Mathematical Sciences
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J. Anusiak, K. P. Shum (1971)
Colloquium Mathematicae
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A. V. Arhangel'skii (2009)
Fundamenta Mathematicae
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Some duality theorems relating properties of topological groups to properties of their remainders are established. It is shown that no Dowker space can be a remainder of a topological group. Perfect normality of a remainder of a topological group is consistently equivalent to hereditary Lindelöfness of this remainder. No L-space can be a remainder of a non-locally compact topological group. Normality is equivalent to collectionwise normality for remainders of topological groups. If a...