Galois connections between closure spaces

TL;DR

This paper extends the concept of Galois connections from posets to closure spaces, broadening their applicability in mathematical contexts.

Contribution

It introduces a novel framework for Galois connections within closure spaces, expanding their theoretical foundation beyond traditional poset settings.

Findings

Established Galois connections in closure spaces

Extended the applicability of Galois theory

Provided new mathematical tools for closure space analysis

Abstract

Galois connections were introduced by Ore and have proved useful in a wide variety of mathematical areas. While Galois connections play on the ground of posets (or more generally of quasiordered sets or qosets), we extend this notion to that of closure spaces.