s_(2)-超连续偏序集  

s_(2)-Supercontinuous Posets

作　　者：张舜 王武[2] ZHANG Shun;WANG Wu(Department of Mathematics,Tianjin Renai College,Tianjin 301636,China;Zhonghuan Information College,Tianjin University of Technology,Tianjin 300380,China)

机构地区：[1]天津仁爱学院数学教学部,天津301636 [2]天津理工大学中环信息学院,天津300380

出　　处：《数学的实践与认识》2024年第6期212-217,共6页Mathematics in Practice and Theory

基　　金：2021年高等学校大学数学教学研究与发展中心教学改革项目(CMC20210115);天津市教委科研计划项目(2023KJ281);远程IO控制技术优化开发(HX23187M)。

摘　　要：将偏序集的超连续性和s_(2)-连续性进行推广,定义了s_(2)^(*)-超连续偏序集,并给出了s_(2)-超连续偏序集和s_(2)^(*)-超连续偏序集的一些等价刻画.主要结果有:1)定义了s_(2)-集并通过其得到了偏序集L为s_(2)-超连续的四个等价刻画;2)给出了s_(2)^(*)-超连续偏序集与s_(2)-连续偏序集之间的关系;3)定义了s_(2)-C-空间,并给出了s_(2)-C-空间与s_(2)^(*)-超连续偏序集的关系.In this paper,we will also generalize the supercontinuous posets and s_(2)-continuous posets and define s_(2)^(*)-supercontinuous posets.Then we obtain some characterization of s_(2)-supercontinuous posets and s_(2)^(*)-supercontinuous posets.The main results are as follows:1)s_(2)-set is defined and some equivalent characterizations of s_(2)-supercontinuous posets are given.2)The relationship between s_(2)^(*)-supercontinuous posets and s_(2)-supercontinuous posets is given.3)The definition of s_(2)-C-spaces and the relationship between s_(2)-C-spaces and s_(2)^(*)-supercontinuous posets are given.

关 键 词：s_(2)-超连续 s_(2)^(*)-超连续 s_(2)-集 s_(2)-C-空间 

分 类 号：O153.1[理学—数学]