A lattice is a mathematical construction built on the notion of a group. First, we review some basic terms. Then we discuss lattices.
For a set S, a relation R is any subset of S × S. For convenience, if (a, b) ∊ R, we write aRb.
The following definitions describe properties of relations.
Definition 30–1. A relation R defined over a set S is reflexive if aRa for all a ∊ S.
Definition 30–2. A relation R defined over a set S is antisymmetric if aRb and bRa ...