Duality theory for convergence groups

R. Beattie and H.-P. Butzmann
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R. Beattie: Mount Allison University, Department of Mathematics and Computer Science
H.-P. Butzmann: Universität Mannheim, Fakultät für Mathematik und Informatik

Chapter Chapter 8 in Convergence Structures and Applications to Functional Analysis, 2002, pp 207-246 from Springer

Abstract: Abstract The well-known Pontryagin — van Kampen duality theorem states that a locally compact, commutative topological group is isomorphic to its second character group, i.e., the character group of its character group. Here each character group carries the compact-open topology. There are various generalizations of this result to not necessarily locally compact, commutative topological groups. Probably the first one was due to S. Kaplan who generalized this result to the product of locally compact commutative topological groups. After some scattered publications, this subject has attracted intensive study once again, see e.g. [Ba91], [Tu], [Ch98], [Au] and [BCMT].

Keywords: Topological Group; Duality Theory; Topological Vector Space; Character Group; Projective Limit (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-015-9942-9_8

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