对称拓扑分子格中的可数S-闭性  

Countable Sclosedness in symmetric topological molecular lattices

作　　者：艾为鸿 

机构地区：[1]抚州师范专科学校数学与计算机科学系

出　　处：《西南师范大学学报（自然科学版）》1998年第1期19-24,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：江西省自然科学基金

摘　　要：对称拓扑分子格（Ｌ，η）称为可数Ｓ闭的，如果其最大元１的由可数半开元组成的覆盖都有有限子族，它们的闭包构成１的覆盖．在上述定义中，若分别将“闭包”换成“半闭包”、将“半开元”换成“强半开元”，就另外得出可数强Ｓ闭的与可数弱Ｓ闭的定义．研究了三种可数Ｓ闭性各自的等价刻划与特征性质，给出它们之间的内在联系．１°（Ｌ，η）是可数Ｓ闭的当且仅当１的每个可数正则闭覆盖都有有限子覆盖．２°在对称拓扑分子格的框架下，可数强Ｓ闭性蕴涵可数Ｓ闭性，可数Ｓ闭性蕴涵可数弱Ｓ闭性．３°在极不连通的对称拓扑分子格中，可数强Ｓ闭性，可数Ｓ闭性与可数弱Ｓ闭性等价． symmetric TML (L,η) is called countable Sclosed,it for every semiopen cover of the greatest element 1 has a finite subcollection whose closures cover 1.In above definition,if “closure” and “semiopen element” are changed with “semiclosure” and “strong semiopen element” respectively,then other definitions of countably strong and weak Sclosed are obtained respectively.It is investigated that equivalent characterization and characteristic properties of three countable Sclosedness.The connections among them are established.Main Results: 1. (L,η) is countable Sclosed iff for every countable regular closed cover of 1 has a finite subcover.2. In symmetric TML,countably strong Sclosedcountable Sclosedcountably weak Sclosed.3.In symmetric TML which is extremally disconnected,countably strong Sclosedness,countable Sclosedness,countably weak Sclosedness are equivalent to each other.

关 键 词：对称拓扑分子格 强半开元 可数S-闭性 序同态 

分 类 号：O153.1[理学—数学] O189.11[理学—基础数学]