Ziqin Feng
Seeking a network characterization of Corson compacta

Comment.Math.Univ.Carolin. 62,4 (2021) 513-521.

Abstract: We say that a collection \mathcal{A} of subsets of X has property (CC) if there is a set D and point-countable collections \mathcal{C} of closed subsets of X such that for any A\in \mathcal{A} there is a finite subcollection \mathcal{F} of \mathcal{C} such that A=D\setminus \bigcup \mathcal{F}. Then we prove that any compact space is Corson if and only if it has a point-\sigma-(CC) base. A characterization of Corson compacta in terms of (strong) point network is also given. This provides an answer to an open question in ``A Biased View of Topology as a Tool in Functional Analysis" (2014) by B. Cascales and J. Orihuela and as in ``Network characterization of Gul'ko compact spaces and their relatives" (2004) by F. Garcia, L. Oncina, J. Orihuela, which asked whether there is a network characterization of the class of Corson compacta.

Keywords: Corson compacta; point network; condition (F); almost subbase; additively \aleph_0-Noetherian

DOI: DOI 10.14712/1213-7243.2022.002
AMS Subject Classification: 54D30 46B50