Vol. 34, No. 2, 1970

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Compact, distributive lattices of finite breadth

Kirby Alan Baker and Albert Robert Stralka

Vol. 34 (1970), No. 2, 311–320

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
Received: 24 June 1968
Published: 1 August 1970
Kirby Alan Baker
Albert Robert Stralka