Displaying similar documents to “List of communications”

Two types of remainders of topological groups

Aleksander V. Arhangel'skii (2008)

Commentationes Mathematicae Universitatis Carolinae

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We prove a Dichotomy Theorem: for each Hausdorff compactification b G of an arbitrary topological group G , the remainder b G ∖ G is either pseudocompact or Lindelöf. It follows that if a remainder of a topological group is paracompact or Dieudonne complete, then the remainder is Lindelöf, and the group is a paracompact p -space. This answers a question in A.V. Arhangel’skii, , Moscow Univ. Math. Bull. 54:3 (1999), 1–6. It is shown that every Tychonoff space can be embedded as a closed subspace...

A study of remainders of topological groups

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...

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...