Basic disconnectedness in bitopological spaces (Q2716692)

Based on the notion of basically disconnectedness for topological spaces the authors introduce the notion of pairwise basically disconnected bitopological spaces: a bitopological space \((X,T_1,T_2)\) is called pairwise basically disconnected iff the \(T_1\)-closure of the \(T_2\)-open \(T_2\)-\(F_\sigma \) set is \(T_2\)-open and the \(T_2\)-closure of each \(T_1\)-open \(T_1\)-\(F_\sigma\) set is \(T_1\) open. In the work equivalent characterizations for these bitopological spaces are given and several properties are investigated.