Characterization of (semi-)Eberlein compacta using retractional skeletons

Claudia Correa, Marek Cúth, Jacopo Somaglia Studia Mathematica 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.

Authors

  • Claudia CorreaCentro de Matemática, Computação e Cognição
    Universidade Federal do ABC
    Avenida dos Estados, 5001
    Santo André, Brazil
    e-mail
    e-mail
  • Marek CúthDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    186 75 Praha 8, Czech Republic
    and
    Institute of Mathematics of the
    Czech Academy of Sciences
    Žitná 25
    115 67 Praha 1, Czech Republic
    e-mail
  • Jacopo SomagliaDipartimento di Matematica “F. Enriques”
    Università degli Studi di Milano
    Via Cesare Saldini 50
    20133 Milano, Italy
    e-mail

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