弱基与度量空间的紧覆盖映像  

Weak Bases and the Compact-Covering Images of Metric Spaces

作　　者：林寿[1,2] 张静[3] 

机构地区：[1]漳州师范学院数学与信息科学系福建漳州363000 [2]宁德师范学院数学研究所福建宁德352100 [3]南京师范大学数学科学学院南京210046

出　　处：《数学物理学报（A辑）》2013年第3期483-493,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10971185,11171162);福建省自然科学基金(2009J01013)资助

摘　　要：借助sn网,获得了拓扑空间X的每一紧子集可度量化且在X中具有可数弱基的等价特征,证明了这空间可刻画为度量空间的1-scc(或scc)的商映像,讨论了每一紧子集具有可数外弱基空间的性质,推广了Michael和Nagami关于度量空间的紧覆盖、开映像的经典结果.In this paper some equivalent conditions of a space in which each compact subset is metrizable and has a countable weak base in the space are obtained by means of sn-networks, the spaces are characterized as images of metric spaces under l-scc （resp. scc） and quotient maps, and spaces in which each compact subset has a countable outer weak base are discussed, which generalized the classic result about compact-covering and open images of metric spaces by Michael and Nagami.

关 键 词：sn网 弱基 外sn网 外弱基 紧覆盖映射 1序列覆盖映射 商映射 1-SCC映 射 SCC映射 

分 类 号：O189.1[理学—数学]