Order isomorphisms between bases of topologies

Abstract

In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have been able to show some results about arbitrary bases in complete metric spaces and also about regular open subsets in Hausdorff regular topological spaces.

Keywords

• Lattices
• complete metric spaces
• locally compact spaces
• open regular sets
• partially ordered sets