分层偏序集上的形式球空间及其完备性  

The Formal Ball Space on Posets with Sheaves and Its Completeness

作　　者：武利刚 WU Li-gang(Department of Mathematics.School of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,China)

机构地区：[1]北京建筑大学理学院数学系,北京102616

出　　处：《模糊系统与数学》2021年第5期47-52,共6页Fuzzy Systems and Mathematics

基　　金：北京建筑大学金字塔人才培养工程-北京建筑大学主讲教师支持计划项目(YXZJ20200301);北京建筑大学教育科学与研究(一般)项目(Y2046)

摘　　要：分层偏序集指的是一个偏序集,且具有其交为已知偏序的按包含递减的偏序族。本文的主要结果:(1)在分层偏序集上定义了形式球空间,(2)该形式球空间是ω-完备的当且仅当分层偏序集是R-完备的且偏序族中的每个偏序均是ω-完备的。A poset with sheaves is a poset whose underlying set carries family of decreasing(with respect to set's inclusion)partial orders,where its intersection is the partial order of the poset.Themain results of the paper are:(1)formal ball space is defined on poset with sheaves,(2)the formalball space is ω-complete if and only if the poset with sheaves is R-complete and every order in thefamily is ω-complete.

关 键 词：偏序集﹔相似度 形式球空间 完备性 

分 类 号：O189[理学—数学] O153[理学—基础数学]