Vol. 54, No. 2, 1974

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Continuous measures, Baire category, and uniform continuity in topological groups

Gerald L. Itzkowitz

Vol. 54 (1974), No. 2, 115–125

In this paper we use an observation of M. Rajagopalan to show that each nondiscrete locally compact topological group can be wlitten as a disjoint union of continuumly many closed nowhere dense Gδ sets. This observation also enables us to give a new constructive proof of a theorem of Kister. We show that in a nondiscrete noncompact locally compact group it is always possible to construct a bounded continuous function that is not left uniformly continuous. Finally this construction motivates a similar construction which yields examples of functions in LUC(G) but not in RUC (G) when G is a nondiscrete and nonunimodular locally compact topological group or when G is a nondiscrete locally compact metric group with inequivalent right and left uniform stmctures.

Mathematical Subject Classification 2000
Primary: 22D05
Received: 8 April 1971
Published: 1 October 1974
Gerald L. Itzkowitz