CONVEX CONTINUOUS LATTICES

In this paper the theory of convex continuous lattices is introduced and its connections with functional analysis are investigated. The motivation for convex continuous lattices arises from the following: The lattice of closed convex subsets of a compact convex subset of a locally-convex topological vector space is known to be a continuous lattice [10]. Moreover, it inherits a convexity structure from the convexity structure on the compact convex subset. This combination forms the basis for the definition of conve