积空间是D -空间的空间类

数学物理学报

积空间是D -空间的空间类

彭良雪

京工业大学应用数理学院北京 100022

收稿日期:2004-10-23 修回日期:2005-12-29 出版日期:2006-10-25 发布日期:2006-10-25
通讯作者: 彭良雪
基金资助:
北京市委组织部优秀人才项目(KW060120037)资助

The Spaces Whose Products is a D -space

Peng Liangxue

College of Applied Science, Beijing University of Technology, Beijing 100022

Received:2004-10-23 Revised:2005-12-29 Online:2006-10-25 Published:2006-10-25
Contact: Peng Liangxue

摘要/Abstract

摘要：

人们知道每个C-似空间是 D -空间, 且每个正则弱θ -可加细 C-散布空间也是D -空间。上述空间类的积空间还是D -空间吗?在这篇文章中作者讨论了该问题, 得到如下结论：正则弱θ -可加细空间的有限积是D -空间；正则Lindel\"of C-散布空间的可数积是D -空间

关键词: 弱 θ -可加细空间, C -散布空间, D -空间, Lindel\"of空间

Abstract: It is known that every C-like space is a D -space, and every regular weakly
θ-refinable C-scattered space is also a D-space.
Is the product of these spaces also a D-space?
In this paper the above question is discussed. It is proved that the finite
product of regular weakly θ-refinable C -scattered
spaces is aD -space, and the countable product
of regular Lindel\"of C-scattered spaces is aD -space

Key words: Weakly θ -refinable, C-scattered space, D -space, ')">Lindel\"of space.

中图分类号:

54D20

彭良雪. 积空间是D -空间的空间类[J]. 数学物理学报, 2006, 26(5): 653-658.

Peng Liangxue. The Spaces Whose Products is a D -space[J]. Acta mathematica scientia,Series A, 2006, 26(5): 653-658.