Minimal extensions of distributive bounded lattices

There is a considerable literature on (proper) maximal sublattices of distributive bounded lattices. In this note, we consider the dual concept of when L' is a minimal extension of L, that is L is a (proper) maximal sublattice of L'. Minimal extensions occur in one of two ways, so-called "removing a cover" or "splitting a point". The removal of covers is characterised and "special points" that can always be split are identified. For infinite L, there are at least vertical bar L vertical bar minimal extensions obtained by splitting special points, and examples are given to show that there need be no other minimal extensions.