Closed subsets of star σ-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 σ-compact space

Subjects:

54D20, 54B10, 54D55

Abstract

In this paper, we prove the following statements:(1) There exists a pseudocompact star σ-compact Tychonoff space having a regular-closed subspacewhich is not star σ-compact.(2) Assuming 20=21, there exists a starcountable (hence star σ-compact) normal space having aregular-closed subspace which is not star σ-compact.

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Published

2013-10-15