Arnautov's problems on semitopological isomorphisms

• Dikranjan, Dikran ^[1] ; Giordano Bruno, Anna ^[1]
  1. [1] Università di Udine
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 1, 2009, págs. 85-119
• Idioma: inglés
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• Resumen

  • Semitopological isomorphisms of topological groups were introduced by Arnautov [2], 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 on G every semitopological isomorphism with domain (G, ) 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.