On some low separation axioms via \(\lambda\)-open and \(\lambda\)-closure operator (Q861986)

A subset of a topological space is called a \(\lambda\)-closed set, if it is an intersection of a closed set and of an intersection of open sets. Using this kind of closedness, the separation axioms \(R_0\) and \(R_1\) are modified to \(\lambda\)-\(R_0\) and \(\lambda\)-\(R_1\). Thus, e.g., \(X\) is a \(\lambda\)-\(R_0\)-space if every \(\lambda\)-open set contains a \(\lambda\)-closure of each of its points. Basic properties and relations for those new separations are studied.