Finitely Presented Lattices: Continuity and Semidistributivity
نویسنده
چکیده
In [3] we investigated finitely presented lattices and the closely related subject of lattices generated by a finite partial lattice. We described a canonical form for the elements of such a lattice and used this to study the covering relation. We showed that there is an effective procedure for finding the covers of any element of a finitely presented lattice. We gave an example of a finitely presented lattice which has no cover at all. In the present paper we use some of the results of [3] to prove two new theorems about finitely presented lattices. We show that such lattices are both upper and lower continuous, generalizing the corresponding result for free lattices which is due to Whitman [7]. We also characterize those finitely presented lattices which are semidistributive.
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