可数sober化  

Countable sobrification

作　　者：龚雅玲 史俊苗 GONG Yaling;SHI Junmiao(Yuzhang Normal University,Nanchang 330103,China;College of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]豫章师范学院,江西南昌330103 [2]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《南昌大学学报（理科版）》2018年第4期322-326,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11361028);江西省教育厅科技基金资助项目(GJJ150344)

摘　　要：对于给定的拓扑空间X,借助于X中的可数既约闭集给出了拓扑空间X的一种可数sober化。证明了拓扑空间X的可数既约集可以诱导出集合X上的一个拓扑,讨论了在该拓扑下的一些性质,特别地证明了可数sober空间上由可数既约集诱导的拓扑与原拓扑一致。For a given topological space X,a method of countable sobrification of Xis proposed in this paper via the countably irreducible closed subsets in X.We prove that the countably irreducible subset in a topological space X can induce a topology in the set Xand we discuss some properties of the topology.In particular,we prove that the topology induced by the countably irreducible subsets in a countably sober space coincides with the original topology.

关 键 词：可数既约集 可数sober化 τCSI-拓扑 

分 类 号：O153[理学—数学] O189[理学—基础数学]