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We say that a collection of subsets of has property if there is a set and point-countable collections of closed subsets of such that for any there is a finite subcollection of such that . Then we prove that any compact space is Corson if and only if it has a point-- 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...
Necessary conditions and sufficient conditions are given for 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 an m₁-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).
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