Compact, distributive lattices of finite breadth

Abstract

Necessary and sufficient conditions are given for a complete distributive lattice with topology to be embeddable in the product of n complete chains, where the embedding is required to be simultaneously algebraic and topological. Corollaries are (i) a characterization of those compact topological lattices which can be embedded in an %-cell and (ii) the fact that breadth provides a bound on the topological dimension for compact, distributive topological lattices of finite breadth.