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