Vol. 52, No. 1, 1974

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Compatible topologies and continuous irreducible representations

Kevin James Sharpe

Vol. 52 (1974), No. 1, 227–231

Suppose there are two locally compact group topologies on a group and that the sets of irreducible unitary representations of the group continuous with respect to each of the topologies coincide. Then the topologies are equal if they are comparable or there is a normal subgroup open and σ-compact in one of the topological groups. This is a result of Klaus Bichteler’s, but the work presented here represents a much shorter method than that used by Bichteler, using little representation theory, but using results involving compatible topologies: Topologies containing in common a Hausdorff topology.

Mathematical Subject Classification 2000
Primary: 22D10
Received: 16 October 1973
Published: 1 May 1974
Kevin James Sharpe