Metric \(\sigma\)-frames versus metric Lindelöf spaces (Q1413438)

The authors introduce the category M\(\sigma\)Frm of metric \(\sigma\)-frames and give the adjoint relation between this category and the category MLSp of metric Lindelöf spaces. Let \(\text{Coz}(X)= 0(X)\), where \(0(X)\) is the frame of open sets of the topological space \(X\). The authors show that Coz is a functor from MLSp to M\(\sigma\)Frm. They define a functor \(\psi\) from M\(\sigma\)Frm to MLSp and show that \(\psi\) is the adjoint to Coz. MLSp is dually equivalent to the category of Alexandroff metric \(\sigma\)-frames.