Mathematics – Group Theory
Scientific paper
2009-11-09
Mathematics
Group Theory
Report for the 24th Summer Conference on Topology and its Applications, Brno, Czech Republic, July 2009
Scientific paper
For Pontryagin's group duality in the setting of locally compact topological Abelian groups, the topology on the character group is the compact open topology. There exist at present two extensions of this theory to topological groups which are not necessarily locally compact. The first, called the Pontryagin dual, retains the compact-open topology. The second, the continuous dual, uses the continuous convergence structure. Both coincide on locally compact topological groups but differ dramatically otherwise. The Pontryagin dual is a topological group while the continuous dual is usually not. On the other hand, the continuous dual is a left adjoint and enjoys many categorical properties which fail for the Pontryagin dual. An examination and comparison of these dualities was initiated in \cite{CMP1}. In this paper we extend this comparison considerably.
Beattie R.
Butzmann H.-P.
No associations
LandOfFree
Continuous and Pontryagin duality of topological groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Continuous and Pontryagin duality of topological groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous and Pontryagin duality of topological groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-660593