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

See also

  • filtered category
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