Valdivia compact Abelian groups

Details Valdivia compact Abelian groups Valdivia compact Abelian groups

2007-06-26

arxiv.org/abs/0706.3772v2

Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. (RACSAM) Vol. 102/2 (2008) 193-197

Mathematics

General Topology

Second version with some corrections; 6 pages

Scientific paper

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.

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