Complete Partial Order

Complete Partial Order

In mathematics, directed-complete partial orders and ω-complete partial orders (abbreviated to dcpo, ωcpo or sometimes just cpo) are special classes of partially ordered sets, characterized by particular completeness properties. Complete partial orders play a central role in theoretical computer science, in denotational semantics and domain theory.

Read more about Complete Partial Order:  Definitions, Examples, Properties, Continuous Functions and Fixpoints

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Complete Partial Order - Continuous Functions and Fixpoints
... Equipped with the pointwise order, this is again a dcpo, and a cpo whenever Q is a cpo ... Thus the complete partial orders with Scott continuous maps form a cartesian closed category ... Every order-preserving self-map f of a cpo (P, ⊥) has a least fixpoint ...

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