分层偏序集上的广义Scott拓扑与不可约拓扑  

Generalized Scott Topology and Irreducible Topology on Posets with Sheaves

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》2018年第2期128-133,共6页Fuzzy Systems and Mathematics

基　　金：北京建筑大学博士科研启动基金资助项目(101102107);北京建筑大学研究生优质课程质量提升(一般)项目

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[10]。本文仿照[1]的思路,在分层偏序集上定义了不可约拓扑,讨论了该拓扑的基本性质,特别是限制到偏序集上即得Scott拓扑。不同于一般偏序集上的Scott拓扑恰为Alexandroff拓扑的不可约拓扑,本文通过例子表明分层偏序集上的广义Scott拓扑并非广义Alexandroff拓扑的不可约拓扑。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. Along the line in , irreducible topology （defined by irreducible sets） is defined on posets with sheaves, several fundamental properties of this topology are investigated, particularly, it＇s Scott topology when restricted to poset. Unlike the fact that Scott topology is exactly the irreducible topology of Alexandroff topology, an example is obtained in the paper to illustrate that gS-topology is not the irreducible topology.

关 键 词：分层偏序集 广义Scott拓扑 不可约拓扑 

分 类 号：O189[理学—数学] O153[理学—基础数学]