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Modular and metric multilattices. (English) Zbl 0833.06011
Summary: A metric multilattice, which is shown to be a generalization of Birkhoff’s metric lattice, is defined. A metric multilattice is modular, and a directed modular multilattice of locally finite length is metrizable.

MSC:
06B99 Lattices
06A99 Ordered sets
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References:
[1] BENADO M.: Les ensembles partiellement ordonnés et le théorème de raffinement le Schreier II. Czechoslovak Math. J. 5(80) (1955), 308-344. · Zbl 0068.25902
[2] BIRKHOFF G.: Lattice Theory. (3rd edition), Amer. Math. Soc, Providence, R. I., 1967. · Zbl 0153.02501
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