directed set

English

Noun

directed set (plural directed sets)

1. (algebra, set theory) 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

• (set with preorder): downward directed set, upward directed set

See also

• filtered category