一致半连续格的理论研究
发布时间：2018-12-07 16:46
【摘要】：摘要：20世纪70年代初D.Scott因理论计算机的语义问题提出了连续格的概念.这标志着经典Domain理论的出现,同时引起了广泛的关注.1989年Ray.Y首先提出格中的半素理想,1997年赵东升利用半素理想在完备格上给出了一种作用在点与点之间的新关系,从而定义了半连续格,2007年曾丽华等又把这种新关系推广到集与集之间,从而定义了拟半连续格.本学位论文利用半素理想引入一致半素集的定义,以此为基础得到一种作用在点与点之间的新关系,从而定义一致半连续格,并对它进行了深入的研究,主要内容如下 第一部分：引入一致半连续格的概念以及它的若干性质,利用一致半素极小集的方法阐述了映射的一致半连续性、保(?)u关系和保一致半素极小集之间的联系,并得到一致半连续格的任意收缩仍是一致半连续格. 第二部分：引入并研究了拟一致半连续格,得到了有限个拟一致半连续格的笛卡尔乘积是拟一致半连续格,给出了拟一致半连续格的逆像是拟一致半连续格的一个充分条件. 第三部分：给出了一致半Scott拓扑的概念,讨论了一致半连续格上的一致半Scott拓扑的一些基本性质.
[Abstract]:Abstract: in the early 1970s D.Scott put forward the concept of continuous lattice because of the semantic problem of theoretical computer. This marks the emergence of the classical Domain theory and has attracted wide attention. In 1989, Ray.Y first proposed semi-prime ideals in lattices. In 1997, Zhao Dongsheng gave a new relationship between points and points by using semi-prime ideals on complete lattices. In 2007, Zeng Lihua extended the new relation between sets and sets, and then defined quasi semicontinuous lattices. In this dissertation, the definition of uniformly semiprime set is introduced by semiprime ideal, and a new relation between point and point is obtained based on it, and then the uniformly semi-continuous lattice is defined, and it is studied deeply. The main contents are as follows: the concept of uniform semi-continuous lattice and its properties are introduced, and the uniform semi-continuity of mapping is discussed by using the method of uniformly semiprime minimal set. The relation between preserving (?) u relation and preserving uniformly semiprime minimal set is obtained, and the arbitrary contraction of uniformly semicontinuous lattice is still uniformly semicontinuous lattice. In the second part, we introduce and study the quasi-uniformly semicontinuous lattice, and obtain that the Cartesian product of the finite quasi uniformly semicontinuous lattice is quasi uniform semicontinuous lattice, and give a sufficient condition that the inverse of the quasi uniformly semicontinuous lattice is quasi uniform semicontinuous lattice. In the third part, the concept of uniform semi Scott topology is given, and some basic properties of uniform semi Scott topology on uniformly semi continuous lattices are discussed.
【学位授予单位】：淮北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O153.1
本文编号：2367484
[Abstract]:Abstract: in the early 1970s D.Scott put forward the concept of continuous lattice because of the semantic problem of theoretical computer. This marks the emergence of the classical Domain theory and has attracted wide attention. In 1989, Ray.Y first proposed semi-prime ideals in lattices. In 1997, Zhao Dongsheng gave a new relationship between points and points by using semi-prime ideals on complete lattices. In 2007, Zeng Lihua extended the new relation between sets and sets, and then defined quasi semicontinuous lattices. In this dissertation, the definition of uniformly semiprime set is introduced by semiprime ideal, and a new relation between point and point is obtained based on it, and then the uniformly semi-continuous lattice is defined, and it is studied deeply. The main contents are as follows: the concept of uniform semi-continuous lattice and its properties are introduced, and the uniform semi-continuity of mapping is discussed by using the method of uniformly semiprime minimal set. The relation between preserving (?) u relation and preserving uniformly semiprime minimal set is obtained, and the arbitrary contraction of uniformly semicontinuous lattice is still uniformly semicontinuous lattice. In the second part, we introduce and study the quasi-uniformly semicontinuous lattice, and obtain that the Cartesian product of the finite quasi uniformly semicontinuous lattice is quasi uniform semicontinuous lattice, and give a sufficient condition that the inverse of the quasi uniformly semicontinuous lattice is quasi uniform semicontinuous lattice. In the third part, the concept of uniform semi Scott topology is given, and some basic properties of uniform semi Scott topology on uniformly semi continuous lattices are discussed.
【学位授予单位】：淮北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O153.1
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