Ordered Topological Spaces and Topological Semilattices

Abstract

<p>In this thesis, we consider the relationship between ordered topological spaces and topological semilattices.</p> <p>We study the structures of ordered topological spaces and give some characterizations of these spaces, one of which is an answer to a question raised in [5]. We also construct two equivalent Wallman type order compactifications.</p> <p>In addition, we describe epireflective subcategories of categories of ordered topological spaces, and in particular compactifications.</p>