ABSTRACT
In the previous chapter we have seen two examples of operators with closure properties. First, when we generate subalgebras of a given algebra A from subsets X of the carrier set A of A, we have a mapping which takes any X C A to a unique subset (X)A of A. This gives a unary operation, or an operator, ( )A : P(A) --÷ P(A) on the power set of A, which we showed has the three closure properties of Theorem 1.3.7. Later we saw that the operator which maps any binary relation 0 on A to the congruence (0)conA generated by 0 also has these same properties. In fact operators with these properties occur in many areas of Mathematics, and are frequently used as a tool to study other structures.
