Displaying similar documents to “Compactness type properties in topological groups”

Extremal pseudocompact Abelian groups: A unified treatment

William Wistar Comfort, Jan van Mill (2013)

Commentationes Mathematicae Universitatis Carolinae

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The authors have shown [Proc. Amer. Math. Soc. 135 (2007), 4039--4044] that every nonmetrizable, pseudocompact abelian group has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology. Here they give a comprehensive, direct and self-contained proof of this result.

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...

On topological and algebraic structure of extremally disconnected semitopological groups

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

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Starting with a very simple proof of Frol’ık’s theorem on homeomorphisms of extremally disconnected spaces, we show how this theorem implies a well known result of Malychin: that every extremally disconnected topological group contains an open and closed subgroup, consisting of elements of order 2 . We also apply Frol’ık’s theorem to obtain some further theorems on the structure of extremally disconnected topological groups and of semitopological groups with continuous inverse. In particular,...

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...