Characterization of (semi-)Eberlein compacta using retractional skeletons
Volume 263 / 2022
Studia Mathematica 263 (2022), 159-198
MSC: Primary 54C15, 46B50; Secondary 54D30, 46B26, 03C30.
DOI: 10.4064/sm200916-28-6
Published online: 22 November 2021
Abstract
We study retractions associated to suitable models in compact spaces admitting a retractional skeleton and find several interesting consequences. Most importantly, we provide a new characterization of Valdivia compacta using the notion of retractional skeletons, which seems to be helpful when characterizing their subclasses. Further, we characterize Eberlein and semi-Eberlein compacta in terms of retractional skeletons and show that our new characterizations give an alternative proof of the fact that a continuous image of an Eberlein compact is Eberlein as well as new stability results for the class of semi-Eberlein compacta, solving in particular an open problem posed by Kubiś and Leiderman.
