@article{Dikranjan_Giordano Bruno_2009, title={Arnautov’s problems on semitopological isomorphisms}, volume={10}, url={https://polipapers.upv.es/index.php/AGT/article/view/1789}, DOI={10.4995/agt.2009.1789}, abstractNote={<p>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.</p>}, number={1}, journal={Applied General Topology}, author={Dikranjan, Dikran and Giordano Bruno, Anna}, year={2009}, month={Apr.}, pages={85–119} }