Ideal resolvability
A~nonempty topological space is resolvable if it contains two disjoint dense subsets. Let \(\mathcal I\) be an ideal of sets in a~topological space \((X,\tau)\). A~set \(A\subseteq X\) is \(\mathcal I\)-dense if for every \(x\in X\) and every open neighbourhood~\(U\) of~\(x\), \(U\cap A\notin\mathcal I\). A~topological space is \(\mathcal I\)-resolvable if it contains two disjoint \(\mathcal I\)-dense subsets. It is maximal \(\mathcal I\)-resolvable if it is \(\mathcal I\)-resolvable and no strictly finer topology is \(\mathcal I\)-resolvable. These and related notions are investigated in the paper. In particular, the resolvability of the density topology is proved.
scientific article; zbMATH DE number 1307867