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Metrizability Conditions for Completely Distributive Lattices
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1983