摘要
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.
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(Nos.10861007,11161023)
the National Excellent Doctoral Dissertation of China(No.2007B14)
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)
关键词
连续偏序集
概念引入
全连续
关系表
广义
等价
晶格
Hypercontinuous posets,Generalized completely continuous posets,Normal completion
