# directed set

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## English[edit]

### Noun[edit]

**directed set** (*plural* **directed sets**)

- (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[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**