- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:48
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
120
2008
0
Semitopological Homomorphisms
Anna
Giordano Bruno
Università di Udine, UDINE, ITALY
Inspired by an analogous result of Arnautov about isomorphisms, we prove that all continuous surjective homomorphisms of topological groups f : G → H can be obtained as restrictions of open continuous surjective homomorphisms f˜ : G˜ → H, where G is a topological subgroup of G˜. In case the topologies on G and H are Hausdorff and H is complete, we characterize continuous surjective homomorphisms f : G → H when G has to be a dense normal subgroup of G˜. We consider the general case when G is requested to be a normal subgroup of G˜, that is when f is semitopological — Arnautov gave a characterization of semitopological isomorphisms internal to the groups G and H. 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 f to be semitopological. Finally we establish a lot of stability properties of the class of all semitopological homomorphisms.
Topological groups, Lie groups
General
79
126
10.4171/RSMUP/120-6
http://www.ems-ph.org/doi/10.4171/RSMUP/120-6