L-序水平一致极限空间

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英文篇名：L-ordered Level Uniform Limit Spaces 作者：王文静 ; 方进明 英文作者：WANG Wenjing;FANG Jinming;School of Mathematical Sciences,Ocean University of China; 关键词：一致极限 ; 笛卡儿闭性 ; L-序一致极限空间 ; L-序水平一致极限空间 ; 双反射子范畴 英文关键词：uniform limit;;Cartesian-closedness;;L-ordered uniform limit spaces;;L-ordered level uniform limit spaces;;bireflective subcategory 中文刊名：SCSD 英文刊名：Journal of Sichuan Normal University(Natural Science) 机构：中国海洋大学数学科学学院; 出版日期：2019-01-11 出版单位：四川师范大学学报(自然科学版) 年：2019 期：v.42 基金：国家自然科学基金(11471297);; 山东省自然科学基金(ZR2017MA017) 语种：中文; 页：SCSD201901005 页数：5 CN：01 ISSN：51-1295/N 分类号：34-38

摘要

基于满层L-滤子的L-包含序,提出L-序一致极限空间的概念,证明L-序一致极限空间范畴作为拓扑范畴是笛卡儿闭的.同时利用"水平结构"的思想,发现了它的水平空间,即L-序水平一致极限空间.在证明L-序水平一致极限空间范畴与L-序一致极限空间范畴是范畴同构的同时,还建立了L-序水平一致极限空间范畴是文献中L-水平一致极限空间范畴的双反射子范畴这一深入联系.
        In this paper,based on the lattice-valued inclusion order relation of stratified L-filters,we propose the concept of L-ordered uniform limit spaces,and show that the category of all L-ordered uniform limit spaces as topological category is Cartesian-closed.Meanwhile,by making use of the idea of "level structure",we find the level space of L-ordered uniform limit spaces,namely L-ordered level uniform limit spaces. We prove that the category of all L-ordered level uniform limit spaces and the category of all L-ordered uniform limit spaces are isomorphism. In the meantime,we establish the connection that the category of all L-ordered level uniform limit spaces is a bireflective subcategory of the category of all L-level uniform limit spaces.

引文

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