directed set

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English[edit]

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Wikipedia

Noun[edit]

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 ac and bc.

Usage notes[edit]

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[edit]

See also[edit]