Uniform normality of topological groups and -groups
Bohumil Šmarda (1982)
Archivum Mathematicum
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Bohumil Šmarda (1982)
Archivum Mathematicum
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Roland Coghetto (2015)
Formalized Mathematics
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Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods...
John Boris Miller (1975)
Compositio Mathematica
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Igor V. Protasov (2002)
Commentationes Mathematicae Universitatis Carolinae
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Answering recent question of A.V. Arhangel'skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.
Yang, J.S. (1980)
International Journal of Mathematics and Mathematical Sciences
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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...