poset

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P = (X, <=), where X is called the ground set of P and <= is the partial order of P. An element u in a partially ordered set (X, <=) is said to be an upper bound for a subset S of X if for every s element S, we have s<=u. Similarly, a lower bound for a subset S is an element l such that for every s element S, l<=s. If there is an upper bound and a lower bound for X, then the poset (X, <=) is said to be bounded.

circle order | cover relation | dominance | ground set | Hasse diagram | interval order | isomorphic posets | lattice-ordered set | order isomorphic | partial order | poset dimension | realizer | relation