Valdivia compact Abelian groups

Abstract

Let R denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of retractions. Class R is striclty larger than the class of Valdivia compact spaces. We show that every compact connected Abelian group which is a topological retract of a space from class R is necessarily isomorphic to a product of metric groups. This completes the result of V. Uspenskij and the author, where a compact connected Abelian group outside class R has been described.

Second version with some corrections; 6 pages

References in corpus (4)

• Small Valdivia compact spaces
• A compact group which is not Valdivia compact
• Compact spaces generated by retractions
• Kadec norms on spaces of continuous functions

Cited by in corpus (1)

• Subgroups of direct products closely approximated by direct sums