Semitopological Homomorphisms

  • Anna Giordano Bruno

    Università di Udine, Italy


Inspired by an analogous result of Arnautov about isomorphisms, we prove that all continuous surjective homomorphisms of topological groups can be obtained as restrictions of open continuous surjective homomorphisms , where is a topological subgroup of . In case the topologies on and are Hausdorff and is complete, we characterize continuous surjective homomorphisms when has to be a dense normal subgroup of .

We consider the general case when is requested to be a normal subgroup of , that is when f is semitopological — Arnautov gave a characterization of semitopological isomorphisms internal to the groups and . In the case of homomorphisms we define new properties and consider particular cases in order to give similar internal conditions which are sufficient or necessary for to be semitopological. Finally we establish a lot of stability properties of the class of all semitopological homomorphisms.

Cite this article

Anna Giordano Bruno, Semitopological Homomorphisms. Rend. Sem. Mat. Univ. Padova 120 (2008), pp. 79–126

DOI 10.4171/RSMUP/120-6