关于空间与映射的注记  

Notes on Spaces and Mappings

作　　者：杨洁 YANG Jie(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 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：《广西师范学院学报（自然科学版）》2018年第1期17-20,共4页Journal of Guangxi Teachers Education University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11471153);宁德师范学院资助项目(2016FZ07)

摘　　要：该文讨论几类拓扑空间的映射性质,主要证明连续映射保持序列可分性,商映射保持kR空间性质,有限到一商映射保持gf可数性,有限到一伪开映射保持点Gδ性质,完备映射逆保持(mod k)可度量性和拟(mod k)可度量性.最后,给出几个例说明一些空间类关于映射的不保持性.In this paper,we mainly discuss the mapping properties of several topological spaces.We prove that continuous mappings preserve sequential separability;quotient mappings preserve k R-spaces;finite-to-one quotient mappings preserve gf-countability;finite-to-one pseudo-open mappings preserve point-Gδproperty;(mod k)-metrizability and quasi-(mod k)-metrizability are inverse invariants of perfect mappings.Finally,some counterexamples are given to illustrate that the mappings don't preserve some topological properties.

关 键 词：序列可数性 广义度量性质 有限到一映射 完备映射 商映射 

分 类 号：O189.1[理学—数学]