A characterization of a certain subclass of \(M_1\)-spaces (Q2776900)

The authors introduce the property () (a space \(X\) has property () if, for each closed nowhere dense subset \(M\) of \(X\) and \(p\) in \(M\), there exists a closure-preserving network \(\beta\) of \(p\) in \(X\) such that \(\text{cl}(B-M)=B\) for each \(B\) in \(\beta\)). NEWLINENEWLINENEWLINETheorem. A space \(X\) is a stratifiable space with property () iff it is an M-space whose closed subsets have closure-preserving open neighborhood bases in \(X\).