Closed subsets of star $\sigma$-compact spaces

Authors

  • Yan-Kui Song Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210046, P.R. China Author

Keywords:

Pseudocompact space, normal space, star-Lindel{ö}f space, star $\sigma$-compact space

Subjects:

54D20, 54B10, 54D55

Abstract

In this paper, we prove the following statements:(1) There exists a pseudocompact star $\sigma$-compact Tychonoff space having a regular-closed subspacewhich is not star $\sigma$-compact.(2) Assuming $2^{\aleph_0}=2^{\aleph_1}$, there exists a starcountable (hence star $\sigma$-compact) normal space having aregular-closed subspace which is not star $\sigma$-compact.

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Published

2013-10-15

Issue

Vol. 65 No. 4 (2013): Vol. 65, Issue 4

Section

Articles

License

Copyright (c) 2013 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.