Scott闭集格的C-代数性及其应用
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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 Ccontinuity,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.
The concept of quasi C-continuity for posets is introduced.In terms of quasi Ccontinuity,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.
引文
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[5]Ho W K,Zhao Dongsheng.Lattices of Scott-closed sets[J].Commentationes Mathematicae Universitatis Carolinae,2009,50(2):297-314.
[6]Zhao Dongsheng,Fan Taihe.Dcpo-completion of posets[J].Theoretical Computer Science,2010,411(22-24):2167-2173.
[7]Yang Jinbo,Luo Maokang.Quasicontinuous domains and generalized completely distributive lattices[J].Advances in Mathematics(China),2007,36(4):399-406.
[8]Jung A.Cartesian closed categories of domains[A].CWI Tract,66.Stichting Mathematisch Centrum,Centrum voor Wiskunde en Informatica[C].Amsterdam,1989.
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[10]Isbell J.Completion of a construction of Johnstone[J].Proceedings of the American Mathematical Society,1982,85(3):333-334.
[2]Scott D S.Continuous lattices[J].Toposes,algebraic geometry and logic,Lecture Notes in Mathematics,1972,274:97-136.
[3]Lawson J D.The duality of continuous posets[J].Houston Journal of Mathematics,1979,5:357-394.
[4]Xu Luoshan.Continuity of Posets via Scott Topology and Sobrification[J].Topology and Its Applications,2006,153:1886-1894.
[5]Ho W K,Zhao Dongsheng.Lattices of Scott-closed sets[J].Commentationes Mathematicae Universitatis Carolinae,2009,50(2):297-314.
[6]Zhao Dongsheng,Fan Taihe.Dcpo-completion of posets[J].Theoretical Computer Science,2010,411(22-24):2167-2173.
[7]Yang Jinbo,Luo Maokang.Quasicontinuous domains and generalized completely distributive lattices[J].Advances in Mathematics(China),2007,36(4):399-406.
[8]Jung A.Cartesian closed categories of domains[A].CWI Tract,66.Stichting Mathematisch Centrum,Centrum voor Wiskunde en Informatica[C].Amsterdam,1989.
[9]Johnstone P T.Scott is not always Sober[J].Continuous Lattices,Lecture Notes in Mathematics,1981,871:282-283.
[10]Isbell J.Completion of a construction of Johnstone[J].Proceedings of the American Mathematical Society,1982,85(3):333-334.