强FS-Poset若干性质的研究  

Resarches on some properties of a strong FS-Poset

作　　者：梁少辉[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《山东大学学报（理学版）》2009年第8期51-55,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10871121)

摘　　要：本文给出强FS-Poset的定义,讨论强FS-Poset的一些性质,证明强FS-Poset不但是连续的,而且是Scott紧的。在强FS-Poset的基础上,给出了强FS-Lattice的概念,探讨强FS-Lattice的若干性质,用函数空间刻划了强FS-Lattice,得到了连续格是强FS-Lattice的充要条件。The definition of strong FS-Posets is given. Some properties of strong FS-Posets axe discussed, and it is proved that strong FS-Posets not only are continuous, but also are Scott. Based on strong FS-Posets, the concept of strong FS-Lattices is given. Some properties of strong FS-Lattices are studied. Strong FS-Lattices are characteristic of the function space. The sufficient and necessary conditions for a continuous lattice to be a strong FS-Lattice are obtained.

关 键 词：单位逼近 强FS-Poset Scott连续映射 连续格 

分 类 号：O153.1[理学—数学]