Abstract
We study the lattice of all (0,1)-sublattices of a distributive lattice L, using certain compatible quasiorders on the Priestley space of L as our principal tool. Special emphasis is put on the case of finite L, where epic sublattices, Frattini sublattices and covers are considered in some detail. We hope to demonstrate that quasiorders may serve as a concept suitable to unify the many different representations of sublattices of L which are found in the literature.
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Schmid, J. Quasiorders and Sublattices of Distributive Lattices. Order 19, 11–34 (2002). https://doi.org/10.1023/A:1015291410777
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DOI: https://doi.org/10.1023/A:1015291410777