s2-连续性的遗传性和映射不变性  

The Hereditary and Invariant Properties of s2-continuity

作　　者：曹曼华 徐晓泉[1] CAO Man-hua;XU Xiao-quan(School of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与信息科学学院

出　　处：《模糊系统与数学》2019年第6期165-172,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11661057);“赣鄱英才555工程”科技领军人才培养计划项目;江西省自然科学基金资助项目(20192ACBL20045)

摘　　要：基于正规完备化算子,本文讨论了s2-连续性和拟连续性的遗传性和映射不变性。主要结果有:(1)s2-连续性,s2-交连续性与拟连续性对弱Scott开集都是可遗传的;(2)s2-连续性,s2-交连续性和s2-拟连续性对弱Scott闭集一般不具有遗传性;(3)s2-连续偏序集的连续收缩与s2-连续偏序集在弱Scott连续的核映射下的像还是s2-连续的;(4)s2-拟连续偏序集的连续收缩与s2-拟连续偏序集在弱Scott连续的核映射下的像仍是s2-拟连续的。In this paper,based on the Dedekind-MacNeille completion operator,the hereditary and invariant properties s2-continuity are discussed.The main results are:(1)s2-continuity,meet s2-continuity and s2-quasicontinuity are hereditary for weak Scott open sets;(2)s2-continuity,meet s2-continuity and s2-quasicontinuity are generally not hereditary for weak Scott close sets;(3)the continuous contraction s2-continuous posets and the image of s2-continuity under the continuous kernel operator with respect to the weak Scott topology are still s2-continuous;(4)the continuous contraction of s2-quasicontinuous posets and the image of s2-quasicontinuity under the continuous kernel operator with respect to the weak Scott topology are still s2-quasicontinuous.

关 键 词：S2-连续偏序集 S2-拟连续偏序集 连续收缩 内核算子 遗传性 

分 类 号：O159[理学—数学]