Arnautov's problems on semitopological isomorphisms

Details Arnautov's problems on semitopological isomorphisms Arnautov's problems on semitopological isomorphisms

2011-05-18

arxiv.org/abs/1105.3649v1

Appl. Gen. Topol. 10 (2009) no. 1, 85-119

Mathematics

Group Theory

23 pages

Scientific paper

Semitopological isomorphisms of topological groups were introduced by Arnautov, who posed several questions related to compositions of semitopological isomorphisms and the groups G (we call them Arnautov groups) such that for every group topology T on G every semitopological isomorphism with domain (G,T) is necessarily open (i.e., a topological isomorphism). We propose a different approach to these problems by introducing appropriate new notions, necessary for a deeper understanding of Arnautov groups. This allows us to find some partial answers and many examples. In particular, we discuss the relation with minimal groups and non-topologizable groups.

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