Overlap Algebras as Almost Discrete Locales

Boolean locales are almost discrete. In fact, spatial Boolean locales are the same thing as discrete spaces. This does not make sense intuitionistically, since (non-trivial) discrete locales fail to be Boolean. We show that Sambin's "overlap algebras" have good enough features to be called "almost discrete locales". Keywords. Strongly dense sublocales, almost discrete spaces, overlap algebras, constructive topology