A constructive Galois connection between closure and interior

TL;DR

This paper constructs an intuitionistically valid Galois connection between closure and interior operators, providing a new perspective on their classical complement-based correspondence.

Contribution

It introduces an intuitionistic version of the classical closure-interior Galois connection, expanding the theoretical framework within constructive logic.

Findings

Established an intuitionistic Galois connection between closure and interior.

Provided a constructive alternative to the classical complement-based correspondence.

All arguments are valid within intuitionistic logic.

Abstract

We construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complement.