A ternary operation in distributive lattices

Abstract

a H 6) U (ft H *) VJ (* H a) a H ft, and dually, x^aKJb. Hence (i) and (iii) are equivalent. DEFINITION. The segment joining a and b is the set of x satisfying any (hence all) of the conditions of Theorem 1 (cf. Duthie [4]); we denote it [a, 6].