Z-子集系统上的若干性质
发布时间：2018-08-12 10:30
【摘要】：本文主要探讨了偏序集上的Z子集系统的若干性质,包括Z -Scott拓扑、Z - Lawson拓扑以及Z - Scott开滤子的一些性质.第一章,引言中给出了本文的研究背景和相关进展,预备知识中给出了偏序集的基本概念,以及本文需要用到的一些基本结果.第二章分为四节.第一节介绍了Z 子集系统以及Z-连续偏序集、双Z-连续偏序集的相关定义.定义了Z-way- below关系,讨论了 Z-连续偏序集上的Z-分配律以及其他一些性质.第二节定义了偏序集上的Z - Scott拓扑、Z - Lawson拓扑以及双Z - Scott拓扑,讨论了 Z - Scott拓扑和双Z - Scott拓扑的一些性质.第三节讨论了偏序集上Z - Scott拓扑、Z - Lawson拓扑的T1分离性,定义了Z 拟连续偏序集,并在Z-拟连续偏序集的基础上讨论了 Z - Scott拓扑、Z - Lawson拓扑的T2分离性,最后讨论了 Z - Lawson拓扑的其他性质.第四节给出Z -Scott开滤子的定义,得到U是Z-Scott开滤子的充分必要条件.定义了集合之间的way - blow关系,并讨论了集合之间的way和Z below- Scott开滤子之间的一些关系.第三章,首先给出了 Z-连续映射,双Z-连续映射,Z - Scott连续映射,双Z - Scott连续映射的定义,并讨论了双Z - Scott连续映射及双Z-连续映射,Z-连续映射与双Z - Scott连续映射之间的关系,给出了双Z - Scott连续映射的充分条件.
[Abstract]:In this paper, we mainly discuss some properties of Z subset system on partial ordered sets, including Z Scott topology Z Lawson topology and Z Scott open filter. In the first chapter, the research background and related progress of this paper are given in the introduction, the basic concept of partial ordered set is given in the preparatory knowledge, and some basic results that need to be used in this paper are also given. The second chapter is divided into four sections. In the first section, we introduce the Z subset system and the definitions of Z continuous partial ordered set and double Z continuous partial order set. The Z-way-below relation is defined, and the Z-distributive law and some other properties on Z-continuous partial ordered sets are discussed. In the second section, we define Z Scott topology, Z Lawson topology and double Z Scott topology on partial ordered set, and discuss some properties of Z Scott topology and double Z Scott topology. In the third section, we discuss the T1 separability of Z Scott topology and Z Lawson topology on the partial ordered set, define Z quasi continuous partial ordered set, and discuss the T2 separation of Z Scott topology and Z Lawson topology on the basis of Z quasicontinuous partial order set. Finally, other properties of Z-Lawson topology are discussed. In the fourth section, the definition of Z -Scott open filter is given, and the necessary and sufficient conditions for U to be Z-Scott open filter are obtained. The way blow relation between sets is defined, and some relations between way and Z below-Scott open filters between sets are discussed. In chapter 3, we first give the definitions of Z continuous mapping, double Z continuous mapping and double Z Scott continuous mapping. The relations between double Z Scott continuous mapping, double Z continuous mapping and double Z Scott continuous mapping are discussed. The sufficient conditions of double Z Scott continuous mapping are given.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.1
本文编号：2178778
[Abstract]:In this paper, we mainly discuss some properties of Z subset system on partial ordered sets, including Z Scott topology Z Lawson topology and Z Scott open filter. In the first chapter, the research background and related progress of this paper are given in the introduction, the basic concept of partial ordered set is given in the preparatory knowledge, and some basic results that need to be used in this paper are also given. The second chapter is divided into four sections. In the first section, we introduce the Z subset system and the definitions of Z continuous partial ordered set and double Z continuous partial order set. The Z-way-below relation is defined, and the Z-distributive law and some other properties on Z-continuous partial ordered sets are discussed. In the second section, we define Z Scott topology, Z Lawson topology and double Z Scott topology on partial ordered set, and discuss some properties of Z Scott topology and double Z Scott topology. In the third section, we discuss the T1 separability of Z Scott topology and Z Lawson topology on the partial ordered set, define Z quasi continuous partial ordered set, and discuss the T2 separation of Z Scott topology and Z Lawson topology on the basis of Z quasicontinuous partial order set. Finally, other properties of Z-Lawson topology are discussed. In the fourth section, the definition of Z -Scott open filter is given, and the necessary and sufficient conditions for U to be Z-Scott open filter are obtained. The way blow relation between sets is defined, and some relations between way and Z below-Scott open filters between sets are discussed. In chapter 3, we first give the definitions of Z continuous mapping, double Z continuous mapping and double Z Scott continuous mapping. The relations between double Z Scott continuous mapping, double Z continuous mapping and double Z Scott continuous mapping are discussed. The sufficient conditions of double Z Scott continuous mapping are given.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.1
【参考文献】
相关期刊论文 前10条
1 高嘉凌;赵彬;;双Z-连续格和双Z-Scott拓扑的性质[J];陕西师范大学学报(自然科学版);2011年04期
2 范丽红;;偏序集上的双Scott拓扑[J];台州学院学报;2009年06期
3 饶三平;徐晓泉;;拟Z-极小集及其应用[J];模糊系统与数学;2008年04期
4 姚丽娟;徐晓泉;;Z-连续偏序集的特征与稠密度[J];江西师范大学学报(自然科学版);2008年03期
5 张春波;徐晓泉;;Z-连续偏序集的映射性质[J];江西科学;2008年03期
6 阮小军;毕含宇;赵洋;;Z-极小集及其对Z-连续偏序集的应用[J];江西师范大学学报(自然科学版);2006年04期
7 李娟;Z-连续偏序集的基[J];宝鸡文理学院学报(自然科学版);2005年04期
8 徐晓泉,罗懋康,黄艳;拟Z-连续domain和Z-交连续domain[J];数学学报;2005年02期
9 徐晓泉,刘应明;Z-拟连续domain上的Scott拓扑和Lawson拓扑[J];数学年刊A辑(中文版);2003年03期
10 覃锋,徐晓泉;广义Z-连续偏序集[J];江西师范大学学报(自然科学版);1999年03期
相关硕士学位论文 前1条
1 李伯权;Z-连续偏序集[D];南京师范大学;2004年
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