Pontryagin Duality for Spaces of Continuous Functions

Spaces of Continuous Functions

Let X be a completely regular topological space, B(X) the Banach space of real-valued bounded continuous functions on X, with the usual norm ||&|| =supa?£x|&(#)| • A subset GCB(X) is called completely regular (c.r.) over X if given any closed subset KQ.X and point XoÇzX — K, there exists a ô £ G such that &(#o) = |NI a n ( i sup^^is: \b(x)\ <||&||. A topological space X is completely regular in...

Reproducing kernel almost Pontryagin spaces

Article history: Received 16 May 2014 Accepted 1 August 2014 Submitted by R. Brualdi MSC: primary 46C20, 46E40 secondary 46E22, 54D35

Topology Proceedings 37 (2011) pp. 315-330: Continuous and Pontryagin duality of topological groups

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 cont...

The Pontryagin duality of sequential limits of topological Abelian groups

We prove that direct and inverse limits of sequences of reflexiveAbelian groups that are metrizable or k -spaces, but not necessarily locally compact, are reflexive and dual of each other provided some extra conditions are satisfied by the sequences. © 2005 Elsevier B.V. All rights reserved. MSC: 22A05; 22D35; 18A30

Sübalgebras of Spaces of Continuous Functions