【摘要】：本文主要探討了偏序集上的Z子集系統(tǒng)的若干性質(zhì),包括Z -Scott拓?fù)�、Z - Lawson拓?fù)湟约癦 - Scott開(kāi)濾子的一些性質(zhì).第一章,引言中給出了本文的研究背景和相關(guān)進(jìn)展,預(yù)備知識(shí)中給出了偏序集的基本概念,以及本文需要用到的一些基本結(jié)果.第二章分為四節(jié).第一節(jié)介紹了Z 子集系統(tǒng)以及Z-連續(xù)偏序集、雙Z-連續(xù)偏序集的相關(guān)定義.定義了Z-way- below關(guān)系,討論了 Z-連續(xù)偏序集上的Z-分配律以及其他一些性質(zhì).第二節(jié)定義了偏序集上的Z - Scott拓?fù)�、Z - Lawson拓?fù)湟约半pZ - Scott拓?fù)?討論了 Z - Scott拓?fù)浜碗pZ - Scott拓?fù)涞囊恍┬再|(zhì).第三節(jié)討論了偏序集上Z - Scott拓?fù)�、Z - Lawson拓?fù)涞腡1分離性,定義了Z 擬連續(xù)偏序集,并在Z-擬連續(xù)偏序集的基礎(chǔ)上討論了 Z - Scott拓?fù)�、Z - Lawson拓?fù)涞腡2分離性,最后討論了 Z - Lawson拓?fù)涞钠渌再|(zhì).第四節(jié)給出Z -Scott開(kāi)濾子的定義,得到U是Z-Scott開(kāi)濾子的充分必要條件.定義了集合之間的way - blow關(guān)系,并討論了集合之間的way和Z below- Scott開(kāi)濾子之間的一些關(guān)系.第三章,首先給出了 Z-連續(xù)映射,雙Z-連續(xù)映射,Z - Scott連續(xù)映射,雙Z - Scott連續(xù)映射的定義,并討論了雙Z - Scott連續(xù)映射及雙Z-連續(xù)映射,Z-連續(xù)映射與雙Z - Scott連續(xù)映射之間的關(guān)系,給出了雙Z - Scott連續(xù)映射的充分條件.
[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.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O153.1

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