Displaying similar documents to “On topological and algebraic structure of extremally disconnected semitopological groups”

Extensions of topological and semitopological groups and the product operation

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 G that is not Dieudonné complete one can find a Dieudonné complete group H such that the Dieudonné completion of G × H is not a topological group containing G × H as a subgroup. Using Korovin’s construction of G δ -dense orbits, we present some examples showing that some results on topological groups are not valid...

Remarks on extremally disconnected semitopological groups

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.