Tolerance extensions in distributive lattices
Josef Niederle · Czech digital mathematics library · 1980
It is known that for every distributive lattice D 9 all congruences on each its sublattice L have extensions on D. An analogous assertion does not hold for compatible tolerances.The aim of this paper is to give answers on questions of the following structure: Let D y L denote distributive lattices, D : L in the relation overlattice: sublattice, let T denote a compatible tolerance on L. Under which conditions set on GIVEN, has T an extension on D for arbitrary VARIABLE?GIVEN and VARIABLE denote all possible combinations of Z), £, T. These combinations are shown in the followingtable: GIVEN DLT DL VARIABLE -T QUESTION NB Q0 Ql *) T cannot exist without L. Answers to the questions Q0,.Q2, Q4 are given in this paper.The question Ql was answered in [3] and the question Q3 in [1].