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In the mathematical fields of order and domain theory, a Scott domain is an algebraic, bounded complete cpo. It has been named in honour of Dana S. Scott, who was the first to study these structures at the advent of domain theory. Scott domains are very closely related to algebraic lattices, being different only in possibly lacking a greatest element. They are also closely related to Scott information systems, which constitute a "syntactic" representation of Scott domains. While the term "Scott domain" is widely used with the above definition, the term "domain" does not have such a generally accepted meaning and different authors will use different definitions; Scott himself used "domain" for the structures now called "Scott domains". Additionally, Scott domains appear with other names like "algebraic semilattice" in some publications. ==Definition== Formally, a non-empty partially ordered set (''D'', ≤) is called a ''Scott domain'' if the following hold: * ''D'' is directed complete, i.e. all directed subsets of ''D'' have a supremum. * ''D'' is bounded complete, i.e. all subsets of ''D'' that have some upper bound have a supremum. * ''D'' is algebraic, i.e. every element of ''D'' can be obtained as the supremum of a directed set of compact elements of ''D''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Scott domain」の詳細全文を読む スポンサード リンク
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