Abstract

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

Keywords: Pseudocompact space; normal space; star-Lindel{ö}f space; star $\sigma$-compact space.

MSC: 54D20, 54B10, 54D55

Pages:  476$-$480     

Volume  65 ,  Issue  4 ,  2013