Displaying similar documents to “Continuous actions of pseudocompact groups and axioms of topological group”

Homomorphic images of ℝ -factorizable groups

Mihail G. Tkachenko (2006)

Commentationes Mathematicae Universitatis Carolinae

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It is well known that every ℝ -factorizable group is ω -narrow, but not vice versa. One of the main problems regarding ℝ -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every ω -narrow group is a continuous homomorphic image of an ℝ -factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an ℝ -factorizable...

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...