Functional Analysis and Time Optimal Control (Enhanced Edition‪)‬

Apartially orderedsystem is a set 9 together with a binary operation
5 , d efined between some elements of 9,w hich satisfies: ( I ) a 5 b and
b _I c implies a 5 c; ( 2 ) a 5 a ; (3) a S b and b 5 a implies a = b. If S
is partially ordered and Q is a subset of B such that a, b E Q implies
either a 5 b or b 5 a then Q is said to be completely (totally) ordered.