Auxiliary and Approximating Relations1
Adam Grabowski · 2004
(1.9–1.19) in [10]. Definitions of Scott’s auxiliary and approximating relations are introduced in this work. We showed that in a meet-continuous lattice, the way-below relation is the intersection of all approximating auxiliary relations (proposition (40) — compare 1.13 in [10, pp. 43–47]). By (41) a continuous lattice is a complete lattice in which ≪ is the smallest approximating auxiliary relation. The notions of the strong interpolation property and the interpolation property are also introduced.