拓扑保持映射下的拓扑性质
Topological properties under topology-preserving mappings
锜茜茜 1林福财1
作者信息
- 1. 闽南师范大学数学与统计学院,福建 漳州 363000
- 折叠
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.
Abstract
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 pre-serving mappings,are dicussed and it is obtained that the connectivity,compactness,paracompact-ness,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Key words
topology preserving mapping/open mapping/closed mapping/density/separable space/paracompact space引用本文复制引用
基金项目
福建省自然科学基金重点项目(2020J02043)
国家自然科学基金(11571158)
出版年
2024
NETL
NSTL
万方数据