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
In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic top...In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset.展开更多
In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to...In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posers.展开更多
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 the National Natural Science Foundation of China(Grant Nos.1167100811101212)the University Science Research Project of Jiangsu Province(Grant No.15KJD110006)
文摘In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10871121, 11001158）
文摘In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posers.
