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关于相对对称度量和1-度量的研究
  • ISSN号：1000-1840
  • 期刊名称：吉林师范大学学报(自然科学版)
  • 时间：0
  • 页码：1-3
  • 语言：中文
  • 分类：O189.1[理学—数学;理学—基础数学]
  • 作者机构：[1]吉林师范大学数学学院,吉林四平136000
  • 相关基金：国家自然科学基金项目：（10571081）
  • 相关项目：序拓扑空间和选择理论以及类紧性的研究
作者： 张国芳|
关键词： Y在X中对称度量化, Y在X中1-度量化, Y在X中严格1-度量化, symmetrizability Y of in X, 1--metrizability of Y in X, strict 1--metrizability of Y in X.
中文摘要：

本文主要对相对对称度量和1-度量给与了研究,得出以下结果：（1）若Y在X中对称度量化,且Y在X中是Lindeloef的,则Y的离散且在X中闭的子空间的基树是可数的。（2）若Y在X中对称度量化且Y的每个离散子空间的基数是可数的,则Y在X中的Souslin数是可数的。（3）如果Y在正则空间X中严格1-度量化,则X在Y上是正规的。

英文摘要：

In this paper, we study some properties of relative symmetrizability and 1-metric and show that the following results： （1）. If Y is symmetrizable in X and Y is Lindelf in X, then the cardinality of every closed in X discrete subspace of Y is countable. of every discrete subspace of Y is countable, then the （2）. If Y is symmetrizable in X and the cardinality Souslin number of Y in X is countable. （3）. If Y is strictly 1-metrizable in a regular space X, then X is normal on Y.

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序拓扑空间和选择理论以及类紧性的研究
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