Hypercontinuous Posets  

作　　者：Wenfeng ZHANG Xiaoquan XU 

机构地区：[1]Department of Mathematics, Sichuan University [2]Department of Mathematics, Jiangxi Normal University

出　　处：《Chinese Annals of Mathematics,Series B》2015年第2期195-200,共6页数学年刊（B辑英文版）

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)

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.

关 键 词：Hypercontinuous posets Generalized completely continuous posets Normal completion 

分 类 号：O153.1[理学—数学] O175.15[理学—基础数学]