Characterization of (semi-)Eberlein compacta using retractional skeletons

Claudia Correa, Marek Cúth, Jacopo Somaglia
2021 Studia Mathematica  
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
more » ... 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.
doi:10.4064/sm200916-28-6 fatcat:smgvkwupv5c5jffsomrbxjkyk4