Let \((X,{\mathcal T},{\mathcal T}^*)\) be an arbitrary bitopological space and \(2^X\) denote the family of \({\mathcal T}\)-closed subsets of \(X\). On \(2^X\) topologies \(L({\mathcal T})\) and \(U({\mathcal T}^*)\) are defined with bases of the form \(\{A\in 2^X \mid A\cap O\neq\emptyset,O\in {\mathcal T}\}\) and \(\{B\in 2^X \mid B\subset G,G\in{\mathcal T}^*\}\), respectively. In the work two specialization orders for a bitopological space \((X,{\mathcal T},{\mathcal T}^*)\) are considered: \(x\leq y\) iff \(x\in{\mathcal T}\)-\(\text{cl}\{y\}\) and \(x\leq^*y\) iff \(x\in{\mathcal T}^*\)-\(\text{cl}\{y\}\). For each subset \(A\subset X\) the operators \(\operatorname {sat}A=\bigcap\{O\in{\mathcal T} \mid A\subseteq O\}\) and \(\operatorname {cosat}A=X\smallsetminus \text{sat}(X\smallsetminus A)\) are defined. The author investigates relationships between properties of the bitopological space \((X,{\mathcal T},{\mathcal T}^*)\) and its hyperspace \((2^X,L({\mathcal T}),U({\mathcal T}^*))\) with respect to separation axioms \(R_0\), \(R_1\) etc.
For the entire collection see [Zbl 0905.00069].