Scott闭集格的C-代数性及其应用  

C-algebraicity of Scott-closed lattices and its applications

作　　者：何青玉[1] 徐罗山[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《高校应用数学学报（A辑）》2014年第3期369-374,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(61103018;61300153)

摘　　要：引入了拟C-连续偏序集的概念,利用拟C-连续性证明了dcpo L是拟连续的当且仅当L上的Scott闭集格是拟连续格.证明了满足性质M的dcpo上的Scott闭集格都是C-代数格,从而给出了具有同构Scott闭集格的两dcpo同构的新的充分条件.The concept of quasi C-continuity for posets is introduced. In terms of quasi C- continuity, it is proved that quasi-continuity of a dcpo is equivalent to the quasi-continuity of its Scott-closed lattice. It is obtained that the Scott-closed lattice of a dcpo satisfying the property M is C-algebraic. A new sufficient condition is given for the isomorphism of two dcpos with isomorphic Scott-closed lattices.

关 键 词：拟C-连续性 C-代数格 性质M SCOTT拓扑 Sober 间 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]