Semitopological isomorphisms of topological groups were introduced by Arnautov, who posed several questions related to compositions of semitopological isomorphisms and about 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.

Arnautov's problems on semitopological isomorphisms

DIKRANJAN, Dikran;GIORDANO BRUNO, Anna
2009

Abstract

Semitopological isomorphisms of topological groups were introduced by Arnautov, who posed several questions related to compositions of semitopological isomorphisms and about 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/880491
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