Continuous Lattices and Convexity Theory

Abstract

<p>This thesis deals with continuous lattices and convexity theory in the following original topics. 1) augmented compact spaces. 2) compact star structures. 3) star lattices. 4) convex continuous lattices.</p> <p>These topics produce plentiful situations where continuous lattices arise from studies of various convexity theories. Conversely, it is shown how the lattices recapture the original theory when they are equipped with the appropriate structure.</p> <p>The theory of augmented compact spaces provides a framework for the succeeding developments. It encompasses not only constructions from convexity theory but also topology and topological algebra.</p> <p>The theories are enriched by numerous examples.</p>