Arnautov's problems on semitopological isomorphisms


  • Dikran Dikranjan Università di Udine
  • Anna Giordano Bruno Università di Udine



A-complete topology, Heisenberg group, Markov group, Minimal group, Open mapping theorem, Permutations group, Semitopological isomorphism, Taımanov topology, Topologizable group


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.


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Author Biographies

Dikran Dikranjan, Università di Udine

Dipartimento diMatematica e Informatica

Anna Giordano Bruno, Università di Udine

Dipartimento diMatematica e Informatica


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How to Cite

D. Dikranjan and A. Giordano Bruno, “Arnautov’s problems on semitopological isomorphisms”, Appl. Gen. Topol., vol. 10, no. 1, pp. 85–119, Apr. 2009.



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