Cones, semicontinuous functions, and continuous lattices (Q1088694)

Standard examples of continuous lattices are spaces of lower semicontinuous functions. In this paper the author introduces a generalization, which he calls a star, of a star-shaped set in a vector space. He shows that the lattice of closed star-shaped subsets for some fixed nucleus is a continuous lattice if the star is compact, and that the lattice of lower semicontinuous functions from a locally compact Hausdorff space to [0,1] can be characterized as the lattice of substars of a compact star from a certain natural class of compact stars.