Difference between revisions 115528838 and 115528839 on dewiki

'''Domain theory''' is a   branch of [[mathematics]] that studies special kinds of [[partially ordered set]]s (posets) commonly called '''domains'''. Consequently, domain theory can be considered as a branch of [[order theory]]. The field has major applications in [[computer science]], where it is used to specify [[denotational semantics]], especially for [[functional programming|functional programming languages]]. Domain theory formalizes the intu(contracted; show full)

== Important results ==

A poset ''D'' is a dcpo if and only if each chain in ''D'' has a supremum. However, directed sets are strictly more powerful than chains.

If ''f'' is a continuous function on a poset ''D'' then it has a least fixed point, given as the least upper bound of all finite iterations of ''f'' on the least element 
''0'': V<sub>n0: ''V''<sub>''n'' in '''N'''</sub> ''f'' <sup>n''n''</sup>(''0''0).

==Generalizations==
*[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.55.903&rep=rep1&type=pdf Synthetic domain theory]
*[http://homepages.inf.ed.ac.uk/als/Research/topological-domain-theory.html Topological domain theory]
*A [[continuity space]] is a generalization of metric spaces and [[poset]]s, that can be used to unify the notions of metric spaces and domains.

==See also==
(contracted; show full)[[Category:Domain theory]]
[[Category:Fixed points]]

[[fa:نظریه دامنه]]
[[fr:Théorie des domaines]]
[[ko:도메인 이론]]
[[ja:領域理論]]
[[zh:域理论]]