【摘要】：摘要：20世紀(jì)70年代初D.Scott因理論計(jì)算機(jī)的語(yǔ)義問(wèn)題提出了連續(xù)格的概念.這標(biāo)志著經(jīng)典Domain理論的出現(xiàn),同時(shí)引起了廣泛的關(guān)注.1989年Ray.Y首先提出格中的半素理想,1997年趙東升利用半素理想在完備格上給出了一種作用在點(diǎn)與點(diǎn)之間的新關(guān)系,從而定義了半連續(xù)格,2007年曾麗華等又把這種新關(guān)系推廣到集與集之間,從而定義了擬半連續(xù)格.本學(xué)位論文利用半素理想引入一致半素集的定義,以此為基礎(chǔ)得到一種作用在點(diǎn)與點(diǎn)之間的新關(guān)系,從而定義一致半連續(xù)格,并對(duì)它進(jìn)行了深入的研究,主要內(nèi)容如下 第一部分：引入一致半連續(xù)格的概念以及它的若干性質(zhì),利用一致半素極小集的方法闡述了映射的一致半連續(xù)性、保(?)u關(guān)系和保一致半素極小集之間的聯(lián)系,并得到一致半連續(xù)格的任意收縮仍是一致半連續(xù)格. 第二部分：引入并研究了擬一致半連續(xù)格,得到了有限個(gè)擬一致半連續(xù)格的笛卡爾乘積是擬一致半連續(xù)格,給出了擬一致半連續(xù)格的逆像是擬一致半連續(xù)格的一個(gè)充分條件. 第三部分：給出了一致半Scott拓?fù)涞母拍?討論了一致半連續(xù)格上的一致半Scott拓?fù)涞囊恍┗拘再|(zhì).
[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.
【學(xué)位授予單位】：淮北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O153.1

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