Order isomorphisms between bases of topologies

TL;DR

This paper investigates the structure of order isomorphisms between bases of topologies, focusing on regular open sets in metric spaces and extending results to broader classes of spaces.

Contribution

It provides new insights into the representations of order isomorphisms between bases, especially in regular open subsets of complete metric and Hausdorff regular spaces.

Findings

Characterization of isomorphisms in regular open subsets of metric spaces

Results extend to arbitrary bases in complete metric spaces

Partial results for regular open subsets of Hausdorff regular spaces

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 achieved some results about arbitrary bases in complete metric spaces and also about regular open subsets of Hausdorff regular topological spaces.