Meaning of partially ordered set | Babel Free

Definitions

1. A set that has a given, elsewhere specified partial order.
   broadly
2. The ordered pair comprising a set and its partial order.
   formal

Examples

“1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28, A partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of "≻" and speak of the partially ordered set P. The ordered fields defined earlier are easily seen to be examples of partially ordered sets.”

“In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set T_M.”

“The invention of a derivative of a finite partially ordered set by Nazarova and Roiter in the late 1960s or early 1970s was a seminal event in the subject of representations of finite partially ordered sets (see [Simson 92]).”

CEFR level