Smyth幂半格及其连续domain表示  

Smyth Power Semilattices and Their Continuous Domain Representations

作　　者：寇辉[1] 刘应明[1] 

机构地区：[1]四川大学数学学院四川,成都610064

出　　处：《数学学报（中文版）》2002年第2期209-214,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家重点基金;国家自然科学基金;数学青年天元基金(TY10125022)资助项目

摘　　要：本文证明了每个Ｓｍｙｔｈ幂半格同构于一连续ｄｃｐｏ的Ｓｍｙｔｈ幂ｄｏｍａｉｎ，而每个连续ｄｃｐｏ同构于其 Ｓｍｙｔｈ幂 ｄｏｍａｉｎ的 ｗａｙ ｂｅｌｏｗ素谱．通过上幂函子建立了连续ｄｏｍａｉｎ与Ｓｍｙｔｈ幂半格之间的范畴等价性，从而揭示了上、下幂ｄｏｍａｉｎ结构之间的联系．In this paper, we prove that every Smyth power semilattice is isomorphic to the Smyth power domain of a continuous dcpo, each continuous dcpo is isomorphic to the way below spetrum of its Smyth power domain, and these two categories are equivalent through the upper power functor, which shows the close connection between upper and lower power domain constructions.

关 键 词：连续dcpo Smyth幂半格 完全分配格 连续DOMAIN 上幂domain 下幂domain 

分 类 号：O153.1[理学—数学] O189.2[理学—基础数学]