The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed w...The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.展开更多
The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual o...The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.展开更多
We introduce the concept of quasi-hyperalgebraic lattice and prove that a complete lattice is a Priestley space with respect to the interval topology if and only if it is quasi-hyperalgebraic. Some characterizations o...We introduce the concept of quasi-hyperalgebraic lattice and prove that a complete lattice is a Priestley space with respect to the interval topology if and only if it is quasi-hyperalgebraic. Some characterizations of quasi-hyperalgebraic lattices are presented. We also prove that the Smyth powerdomain of a quasi-hyperalgebraic lattice is hyperalgebraic.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10331010, 10861007)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 2007B14)+2 种基金the Jiangxi Provincial Natural Science Foundation of China (Nos. 0411025, 2007GZS0179)the Foundation of the Education Department of Jiangxi Province (No. GJJ08162)the Doctoral Fund of Jiangxi Normal University
文摘The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.
基金supported by the National Natural Science Foundation of China(Nos.10861007,11161023)the National Excellent Doctoral Dissertation of China(No.2007B14)+1 种基金the Ganpo 555 Programme for Leading Talents of Jiangxi Province,the Natural Science Foundation of Jiangxi Province(No.20114BAB201008)the Fund of Education Department of Jiangxi Province(No.GJJ12657)
文摘The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.
基金Supported by NSFC(10331010)Research Fund for the Doctoral Program of Higher Education
文摘We introduce the concept of quasi-hyperalgebraic lattice and prove that a complete lattice is a Priestley space with respect to the interval topology if and only if it is quasi-hyperalgebraic. Some characterizations of quasi-hyperalgebraic lattices are presented. We also prove that the Smyth powerdomain of a quasi-hyperalgebraic lattice is hyperalgebraic.
