弱基与度量空间的紧覆盖映像

数学物理学报 ›› 2013, Vol. 33 ›› Issue (3): 483-493.

弱基与度量空间的紧覆盖映像

林寿^1,2|张静³

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 |21004

收稿日期:2011-10-13 修回日期:2013-02-05 出版日期:2013-06-25 发布日期:2013-06-25
基金资助:
国家自然科学基金(10971185, 11171162)和福建省自然科学基金(2009J01013)资助

Weak Bases and the Compact-Covering Images of Metric Spaces

LIN Shou^1,2, ZHANG Jing³

1.Department of Mathematics and |Information Science, Zhangzhou Normal University, Zhangzhou 363000;
2.Institute of Mathematics, Ningde Normal University, Ningde 352100;
3.Institute of Mathematics, Nanjing Normal University, Nanjing 210046

Received:2011-10-13 Revised:2013-02-05 Online:2013-06-25 Published:2013-06-25
Supported by:
国家自然科学基金(10971185, 11171162)和福建省自然科学基金(2009J01013)资助

摘要/Abstract

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.

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

Abstract:

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 1-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.

Key words: sn-networks, Weak bases, Outer sn-networks, Outer weak bases, Compact-covering maps, 1-sequence-covering maps, Quotient maps, 1-scc-maps, scc-maps

中图分类号:

54C10

林寿, 张静. 弱基与度量空间的紧覆盖映像[J]. 数学物理学报, 2013, 33(3): 483-493.

LIN Shou, ZHANG Jing. Weak Bases and the Compact-Covering Images of Metric Spaces[J]. Acta mathematica scientia,Series A, 2013, 33(3): 483-493.