几类度量空间映像的研究  

Workshop Lecture on the Images of Some Metric Spaces

作　　者：林寿[1,2] 朱忠景[1] 

机构地区：[1]漳州师范学院数学与信息科学系,漳州福建363000 [2]宁德师范学院数学研究所,宁德福建352100

出　　处：《数学进展》2013年第2期129-137,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金资助项目(No.10971185;No.11171162)

摘　　要：本文以1961年Alexandroff提出的映射与空间相互关系的思想为线索,有选择地介绍一些关于度量空间映像研究的新老问题及其结果,主要围绕序列覆盖映射的引入及其作用展开讨论,介绍某些弱第一可数空间类,如序列空间、Frechet空间、强Frechet空间、严格Frechet及其双序列空间等与度量空间的映射联系,阐述用映射刻画空间的精髓,彰显布拉格拓扑学会议的持久魅力.In this paper, some old and new problems and results are stated on the images of metric spaces according ＇to the idea with respect to mutual relation of mappings and spaces which was posed by Alexandroff in 1961. It introduces and develops the theory of sequencecovering maps, discusses the relations between the class of weakly first countable spaces（for example, sequential spaces, Frechet spaces, strongly Frechet spaces, strictly Frechet spaces and biequential spaces） and metric spaces by mappings, and describes the essence of characterizing spaces through mappings, which highlights the enduring charm of the Prague Topological Symposium.

关 键 词：Alexandroff设想 序列覆盖映射 可数双商映射 强Frechet空间 第一可数空间 

分 类 号：O189.1[理学—数学]