English

A constructive Galois connection between closure and interior

Logic 2012-03-23 v2 Category Theory General Topology

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.

Cite

@article{arxiv.1101.5896,
  title  = {A constructive Galois connection between closure and interior},
  author = {Francesco Ciraulo and Giovanni Sambin},
  journal= {arXiv preprint arXiv:1101.5896},
  year   = {2012}
}

Comments

This is a revised version. Content is reorganized so to separate clearly what requires an impredicative proof from what can be proven also predicatively. Moreover, some results are given in a more general form and some counterexamples are added

R2 v1 2026-06-21T17:19:11.801Z