On topological and algebraic structure of extremally disconnected semitopological groups

Aleksander V. Arhangel'skii

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&#039;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 $G \times H$ is not a topological group containing $G \times H$ 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.

On a theorem of W.W. Comfort and K.A. Ross

Aleksander V. Arhangel'skii (1999)

Commentationes Mathematicae Universitatis Carolinae

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A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is $C$ -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group $G$ and prove that every $G_{δ}$ -dense subspace $Y$ of a topological group...