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Metrizability Conditions for Completely Distributive Lattices

Published online by Cambridge University Press:  20 November 2018

G. Gierz ,
J. D. Lawson  and
A. R. Stralka
G. Gierz
Affiliation:
University of California at Riverside, California 92521
J. D. Lawson
Affiliation:
University of California at Riverside, California 92521
A. R. Stralka
Affiliation:
Louisana State University, Baton RougeLA, 70808
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Abstract

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A lattice is said to be essentially metrizable if it is an essential extension of a countable lattice. The main result of this paper is that for a completely distributive lattice the following conditions are equivalent: (1) the interval topology on L is metrizable, (2) L is essentially metrizable, (3) L has a doubly ordergenerating sublattice, (4) L is an essential extension of a countable chain.

Keywords

06D1006B3054H12
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 4 , 01 December 1983 , pp. 446 - 453
Copyright
Copyright © Canadian Mathematical Society 1983

References

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