局部连续Domain理论的研究

发布时间：2018-05-13 18:13

本文选题：局部基 + 稠密子集　；参考：《淮北师范大学》2017年硕士论文

【摘要】：Domain理论从上世纪70年代以来,一直受到计算机科学及数学领域的关注.Domain理论研究的对象是满足一定条件的偏序集与它们之间的映射,研究的一个内容是将连续格的理论推广到更为一般的格序结构.本文主要研究工作如下:1.基于连续Domain理论,深入研究了局部连续Domain的相关概念及其理论.首先引入了局部邻域的定义,并在此基础上给出了局部连续Domain的内部刻画;然后借助局部定向集,给出局部连续Domain基、权的定义以及其若干等价刻画;同时探讨局部Scott Domain与拓扑空间(?)的权之间的关系.2.主要研究了局部连续Domain的特征与浓度.首先,在局部基和稠密子集的基础上,定义了局部连续Domain的特征与浓度;其次,探讨了局部连续Domain及其带上Scott拓扑或局部Lawson拓扑时的拓扑空间的特征、浓度之间的关系.3.基于局部半连续格,利用局部半素理想定义了局部半素基,并给出了局部半连续格的局部半素基和左伴随的一些性质.4.给出局部相容半连续格的概念,并借助局部相容半素极小集来阐述映射的局部相容半连续性、保?lc关系及保局部相容半素极小集之间的联系.
[Abstract]:Since the 1970s of the last century, Domain theory has been concerned by the computer science and mathematics field. The object of the study is the mapping between the partial ordered set which satisfies some conditions and the mapping between them. One of the contents of this study is to extend the theory of continuous lattices to more general lattice ordered structures. The main research work of this paper is as follows: 1. Based on the theory of continuous Domain, the related concepts and theories of local continuous Domain are studied in depth. Firstly, the definition of local neighborhood is introduced, and then the interior characterization of local continuous Domain is given, and then the definition of local continuous Domain basis, weight and some equivalent characterizations are given with the help of local orientation set. Local Scott Domain and topological space are also discussed. The relationship between the rights of. The characteristics and concentration of local continuous Domain are studied. Firstly, on the basis of local basis and dense subset, the characteristics and concentrations of locally continuous Domain are defined, and then, the characteristics of locally continuous Domain and its topological space with Scott topology or local Lawson topology are discussed. Based on locally semicontinuous lattices, the local semicontinuous bases are defined by using locally semicontinuous ideals, and some properties of local semicontinuous lattices and left adjoint are given. The concept of locally compatible semicontinuous lattices is given, and the relations among locally compatible semicontinuity, preserving lc relation and locally compatible semiprime minimal sets of mappings are discussed by means of locally compatible semiprime minimal sets.
【学位授予单位】：淮北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.1

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