directed set

Noun

 * 1)  A set equipped with a preorder such that for any two elements a and b there is an element c such that a ≤ c and b ≤ c.

Usage notes
Depending on the interpretation of the preorder (or choice of symbol in the definition), the term may be qualified as upward directed set or downward directed set.

Synonyms

 * downward directed set, upward directed set