Complete partial ordered sets (CPOs)

Defintion

A partially ordered set (D,\sqsubseteq) is a complete partial order (CPO) if it has a bottom element and a least upper bound for each directed subset A \subseteq D.

1. \bot \in D
2. \bigsqcup A \in D for each directed subset A \subseteq D.

See Also

• Compact Element (of a CPO)

References

Hitzler, P., & Seda, A. (2011). Mathematical Aspects of Logic Programming Semantics (1st ed.). CRC Press. https://doi.org/10.1201/b10397

Davey, B.A. and Priestley, H.A. (2002) Introduction to Lattices and Order. 2nd edn. Cambridge: Cambridge University Press.