拓扑保持映射下的拓扑性质  

Topological properties under topology-preserving mappings

作　　者：锜茜茜 林福财 QI Xixi;LIN Fucai(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2024年第1期94-98,共5页Journal of Minnan Normal University：Natural Science

基　　金：福建省自然科学基金重点项目(2020J02043);国家自然科学基金(11571158)。

摘　　要：讨论在拓扑保持映射定义下的拓扑性质,得到了在T0分离公理的假设下拓扑保持映射是同胚映射.此外,还讨论拓扑保持映射下几类基数不变量,并得到拓扑保持映射保持连通性、紧性、仿紧性、可数紧性等.The topological properties under the definition of topologically preserving mappings are discussed.And it is obtained that topologically preserving mappings are homeomorphisms under the assumption of T0 separation axiom.Moreover,some cardinality invariants under topologically preserving mappings,are dicussed and it is obtained that the connectivity,compactness,paracompactness,countable compactness are preserved by topologically preserving mappings.

关 键 词：拓扑保持映射 开映射 闭映射 稠密度 可分空间 仿紧空间. 

分 类 号：O189[理学—数学]