Electronic Version 17 (1992), 335-342

Dikran N. Dikranjan and Dmitri B. Shakhmatov

A topology T on a group G is a group topology if both group operations of G, (g,h) --> g ·h and g --> g^-1, are T-continuous, i.e. if (G, T) is a topological group. In what follows all topological groups and group topologies considered are assumed to be Hausdorff. In 1944 Halmos [12] asked for a characterization of the Abelian groups admitting a compact group topology. This problem was partially resolved by Kaplansky [15] and completely by Harrison [13] and Hulanicki [14]. We investigate the following ``heir'' of Halmos' question:

1  Problem. Which infinite groups admit a (necessarily non-discrete) pseudocompact group topology? Or equivalently, what special algebraic properties must pseudocompact groups have? (A topological space is pseudocompact if every real-valued continuous function defined on it is bounded.)

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volume 17: table of contents
topology proceedings Electronic Version