Chain conditions and star covering properties

Abstract

Whenever P is a topological property, we say that a topological space X is star P if whenever U is an open cover of X, there is a subspace Y⊂X with property P such that St(Y,U)=X. We study the relationships of star P properties for P∈{DCCC,weakly Lindelöf,CCC} with other chain conditions. By using Erdös–Radó's theorem, we also establish several cardinal inequalities for star CCC spaces.