Compact, distributive lattices of finite breadth

Kirby Alan Baker and Albert Robert Stralka

Vol. 34 (1970), No. 2, 311–320

DOI: 10.2140/pjm.1970.34.311

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 n-cell and (ii) the fact that breadth provides a bound on the topological dimension for compact, distributive topological lattices of finite breadth.

Mathematical Subject Classification

Primary: 06.65

Secondary: 20.00

Milestones

Received: 24 June 1968

Published: 1 August 1970