Weak relative pseudo-complements of closure operators

Abstract

We define the notion of weak relative pseudo-complement on meet semi-lattices, and we show that it is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main result is that if a complete lattice ℒ is meet-continuous, then every closure operator on ℒ admits weak relative pseudo-complements with respect to continuous closure operators on ℒ.