A pointfree theory of Pervin spaces

We lay down the foundations for a pointfree theory of Pervin spaces. A space is set equipped with bounded sublattice its powerset, and it known that these objects characterize those quasi-uniform spaces are transitive totally bounded. The notion space, which we call Frith frame, consists frame generating sublattice. In this paper introduce study category frames show classical dual adjunction between topological extends to frames. Unlike what happens spaces, do not have an equivalence categories frames, but latter full coreflective subcategory former. also explore completeness inherited from providing characterization complete description completion arbitrary frame.