Characterization of (semi-)Eberlein compacta using retractional skeletons

0553330 - MÚ 2023 RIV PL eng J - Článek v odborném periodiku
Correa, C. - Cúth, Marek - Somaglia, J.
Characterization of (semi-)Eberlein compacta using retractional skeletons.
Studia mathematica. Roč. 263, č. 2 (2022), s. 159-198. ISSN 0039-3223. E-ISSN 1730-6337
Grant CEP: GA ČR(CZ) GJ19-05271Y
Institucionální podpora: RVO:67985840
Klíčová slova: retractional skeleton * projectional skeleton * Eberlein compact
Obor OECD: Pure mathematics
Impakt faktor: 0.8, rok: 2022
Způsob publikování: Omezený přístup
https://dx.doi.org/10.4064/sm200916-28-6

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.
Trvalý link: http://hdl.handle.net/11104/0328287