  A convexity space is a set X with a chosen family of subsets (called convex
subsets) that is closed under arbitrary intersections and directed unions.
There is a lot of interest in spaces that have both a convexity space and a
topological space structure. In this paper, we study the category of
topological convexity spaces and extend the Stone duality between coframes and
topological spaces to an adjunction between topological convexity spaces and
sup-lattices. We factor this adjunction through the category of preconvexity
spaces (somtimes called closure spaces).
