Meets of Spatial Sublocales (Report‪)‬

1 Introduction and preliminaries Recall that a frame A is a complete lattice satisfying the infinite distributive law a [conjunction] [??] S = [??]{a [conjunction] s|s [member of] S} for all a [member of] A and S [subset or equal to] A. Let A, B be frames, f : A [right arrow] B is a frame morphism if f preserves arbitrary joins and finite meets. We write Frm for the category of frames and frame morphisms and Loc for its dual category whose objects are extensionally the same thing, whose morphisms go in the opposite direction, and write O(X) for the corresponding frame of a locale X.