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Seeking a network characterization of Corson compacta

Ziqin Feng — 2021

Commentationes Mathematicae Universitatis Carolinae

We say that a collection 𝒜 of subsets of X has property ( C C ) if there is a set D and point-countable collections 𝒞 of closed subsets of X such that for any A 𝒜 there is a finite subcollection of 𝒞 such that A = D . Then we prove that any compact space is Corson if and only if it has a point- σ - ( C C ) 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...

Function spaces and local properties

Ziqin FengPaul Gartside — 2013

Fundamenta Mathematicae

Necessary conditions and sufficient conditions are given for C p ( X ) to be a (σ-) m₁- or m₃-space. (A space is an m₁-space if each of its points has a closure-preserving local base.) A compact uncountable space K is given with C p ( K ) an m₁-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).

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