Compactness in abelian topological groups

Rangachari Venkataraman

Vol. 57 (1975), No. 2, 591–595

DOI: 10.2140/pjm.1975.57.591

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,t_i)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