\(D\)-spaces and the associated topology (Q1911888)

A topological space \(X\) is called resolvable if there are two disjoint dense subsets of \(X\), otherwise \(X\) is said to be irresolvable. In this paper the authors investigate these notions from an algebraic viewpoint, i.e. by the use of a suitable binary relation on the power set of a given set \(X\). They are able to show that resolvable, irresolvable and open hereditarily irresolvable spaces can be characterized by certain properties of that binary relation.