Pseudocompact topological group refinements of maximal weight

Comfort, W.; Galindo, Jorge

doi:10.1090/S0002-9939-02-06650-9

Pseudocompact topological group refinements of maximal weight
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by W. W. Comfort and Jorge Galindo PDF

Proc. Amer. Math. Soc. 131 (2003), 1311-1320 Request permission

Abstract:

It is known that a compact metrizable group admits no proper pseudocompact topological group refinement. The authors show, in contrast, that every (Hausdorff) pseudocompact Abelian group $G=(G,\mathcal {T})$ of uncountable weight $\alpha$, satisfying any of the following conditions, admits a pseudocompact group refinement of maximal weight (that is, of weight $2^{|G|}$):

[(i)] $G$ is compact;
[(ii)] $G$ is torsion-free with $\alpha \leq |G|=|G|^\omega$;
[(iii)] [GCH] $G$ is torsion-free.

Remark. (i) answers a question posed by Comfort and Remus [Math. Zeit- schrift 215 (1994), 337–346].

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