A discrete duality between apartness algebras and apartness frames
Ivo Düntsch, Ewa S. Orłowska · Journal of Applied Non-Classical Logics · 2008
Apartness spaces were introduced as a constructive counterpart to proximity spaces which, in turn, aimed to model the concept of nearness of sets in a metric or topological environment. In this paper we introduce apartness algebras and apartness frames intended to be abstract counterparts to the apartness spaces of (Bridges et al., 2003), and we prove a discrete duality for them.