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弱基与度量空间的紧覆盖映像
  • ISSN号：1003-3998
  • 期刊名称：《数学物理学报：A辑》
  • 时间：0
  • 分类：O189.1[理学—数学;理学—基础数学]
  • 作者机构：[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
  • 相关基金：国家自然科学基金（10971185,11171162）和福建省自然科学基金（2009J01013）资助
作者： 林寿[1,2], 张静[3]
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, sn-networks, Weak bases, Outer sn-networks, Outer weak bases, Compact-covering maps, 1-sequence-covering maps, Quotient maps, 1-scc-maps, scc-maps.
中文摘要：

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1-8CC（或8CC）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．

英文摘要：

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.

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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:5382