Pseudocompact groups: progress and problems

Abstract

Several months ago the speaker and Jan van Mill gave a proof of this result [W.W. Comfort, J. van Mill, Extremal pseudocompact abelian groups are compact metrizable, Abstracts Amer. Math. Soc. 27 (2006) 78 (Abstract #1014-22-958); W.W. Comfort, J. van Mill, Extremal pseudocompact abelian groups are compact metrizable, Proc. Amer. Math. Soc. 135 (2007) 4039–4044]: A pseudocompact abelian group of uncountable weight admits both a proper dense pseudocompact subgroup and a strictly larger pseudocompact group topology. This presentation will describe both the necessary new details of the argument and the historical development (useful tools, special cases). Among those who contributed essentially are: K.A. Ross (1964, 1966); T. Soundararajan (1982); L.C. Robertson (1982, 1988); J. van Mill (1989); J. van Mill and H. Gladdines (1994); J. Galindo (2002). Several related unsolved problems will be cited.