Displaying similar documents to “On a theorem of W.W. Comfort and K.A. Ross”

Moscow spaces, Pestov-Tkačenko Problem, and C -embeddings

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

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We show that there exists an Abelian topological group G such that the operations in G cannot be extended to the Dieudonné completion μ G of the space G in such a way that G becomes a topological subgroup of the topological group μ G . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions...

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...