Geodesic
Metrizability Conditions for Completely Distributive Lattices
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 446-453

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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.
DOI : 10.4153/CMB-1983-073-9
Mots-clés : 06D10, 06B30, 54H12 
Gierz, G.; Lawson, J. D.; Stralka, A. R. Metrizability Conditions for Completely Distributive Lattices. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 446-453. doi: 10.4153/CMB-1983-073-9
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     author = {Gierz, G. and Lawson, J. D. and Stralka, A. R.},
     title = {Metrizability {Conditions} for {Completely} {Distributive} {Lattices}},
     journal = {Canadian mathematical bulletin},
     pages = {446--453},
     year = {1983},
     volume = {26},
     number = {4},
     doi = {10.4153/CMB-1983-073-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-073-9/}
}
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