Characterization of (semi-)Eberlein compacta using retractional skeletons
Abstract
We deeply 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 its 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 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 Kubis and Leiderman.
Cite
@article{arxiv.2009.07902,
title = {Characterization of (semi-)Eberlein compacta using retractional skeletons},
author = {Claudia Correa and Marek Cúth and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2009.07902},
year = {2022}
}
Comments
changes from v1: one more equivalent condition added resulting in applications; namely, we obtained new stability results concerning the class of semi-Eberlein comapacta; using this new equivalent condition we also solved a large part of Question 46 from v1 so we removed it from v2; we removed from v2 results from v1 related to the special case of spaces having weight omega_1