Editing Domain theory (section)

== Important results ==
A poset ''D'' is a dcpo if and only if each chain in ''D'' has a supremum. (The 'if' direction relies on the [[axiom of choice]].)

If ''f'' is a continuous function on a domain ''D'' then it has a least fixed point, given as the least upper bound of all finite iterations of ''f'' on the least element ⊥:

:<math> \operatorname{fix}(f) = \bigsqcup_{n \in \mathbb{N}} f^n(\bot)</math>.

This is the [[Kleene fixed-point theorem]].  The <math>\sqcup</math> symbol is the [[Join and meet|directed join]].