LOCALLY CONVEX PROJECTIVE LIMIT CONES

Using a family of ordered cones, we define a suitable order to investigate projective limit topologies for cones. Under the strict separation property, the projective limit cone topology is proved to be equivalent to some of the X-topologies embedded on a subcone of the product cone in its topology. Also, we discuss the cones of convex subsets in projective limits; in particular, we show that a cone of convex subsets of the projective limit cone in its topology carries the projective limit of the cones of convex subsets in its components.