Extremal Problems Concerning Pseudocompact groups
by
Jorge Galindo
Universidad Jaume I
Coauthors: W. W. Comfort (Wesleyan University)

It is known that every (Hausdorff) totally bounded group topology T on an Abelian group G is the topology T_A induced on G by the (point-separating) group A of T-continuous homomorphisms from G to the circle group T. Further, every pseudocompact group is totally bounded. These results from the 1960's suggest the following general question: For what point-separating groups A of H := Hom(G, T) is T_A pseudocompact? Given A subset H such that <G, T_A> is pseudocompact and given f in H\A, we find a workable criterion on f necessary and sufficient that T_B be pseudocompact, with B:=<A \cup {f}>. Then we show, answering a question of Comfort and Remus [Math. Zeitschrift 215 (1994), 337-346], that every compact group topology on Abelian G has a pseudocompact refinement of maximal weight, i.e., of weight 2^|G|.

This work is related to the question of the existence of pseudocompact topological groups <G, T> of uncountable weight which are extremal in the sense that there is no pseudocompact group topology on G stronger than T, or no proper dense pseudocompact subgroup of G. We obtain new classes of non-extremal pseudocompact groups.

Date received: June 1, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-31.