Vol. 57, No. 2, 1975

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Compactness in abelian topological groups

Rangachari Venkataraman

Vol. 57 (1975), No. 2, 591–595
Abstract

If an abelian topological group (G,t) satisfies Pontryagin duality, then the t-compact subsets and the weak compact subsets coincide. Hence if t1,t2 are group topologies on an abelian.group G such that (G,ti)i = 1,2 satisfy Pontryagin duality and have the same set of continuous characters, then t1 = t2.

Mathematical Subject Classification 2000
Primary: 22D35
Milestones
Received: 13 December 1974
Revised: 4 February 1975
Published: 1 April 1975
Authors
Rangachari Venkataraman