Difference between revisions 115528837 and 115528838 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)

===Way-below relation===

A more elaborate approach leads to the definition of the so-called '''order of approximation''', which is more suggestively also called the '''way-below relation'''. An element ''x'' is ''way below'' an element ''y'', if, for every directed set ''D'' with supremum such that

:''y'' ≤ 
''sup ''D'',

there is some element ''d'' in ''D'' such that 

:''x'' ≤ ''d''.

Then one also says that ''x'' ''approximates'' ''y'' and writes 

(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]]