Fitness and subfitness via interior and closure operators

Abstract

We start by rephrasing some well-known characterizations of fit and subfit locales in terms of closure and interior operators on the system of sublocales. Using these characterizations, we are able to extend the notions of fitness and subfitness to a more general setting. This approach not only allows us to obtain more general results, but also to present new properties of fitness and subfitness (such as a formula for the computation of supplements of sublocales). Using this approach we were also able to simplify the proofs of some well-known results.