Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (2): 358-363.

• Articles • Previous Articles     Next Articles

On CSS Spaces and Related Conclusions

PENG Liang-Xue, WANG Li-Xia   

  1. College of Applied Science, Beijing University of Technology, Beijing 100124
  • Received:2008-10-15 Revised:2009-09-15 Online:2010-04-25 Published:2010-04-25
  • Supported by:

    北京市教育委员会科技发展计划面上项目(KM200810005024)和教育部留学回国人员科研启动基金资助.

Abstract:

A space X is a CSS space if  compact sets are uniformly Gδ sets. In the first part of this note, the authors mainly prove that, if a space X has a quasi-Gδ (2) diagonal, then X is a CSS space. They also show that the  countable product of CSS spaces is a CSS space, and if $X$ is the union of a family of countable closed CSS subspaces, then X is a CSS space. In the second part, the authors mainly show that, if X is the union of a family of countable closed β-subspaces (semi-stratifiable spaces), then X is a β-space (semi-stratifiable space).

Key words: CSS space, Quasi-Gδ(2) diagonal, g function,  β-space

CLC Number: 

  • 54E20
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