Commun. Korean Math. Soc. 2007 Vol. 22, No. 4, 569-573 Printed December 1, 2007

Yan-Kui Song Nanjing Normal University

Abstract : In this note, we construct an example of a Hausdorff $\mathcal K$-starcompact (hence,$1\frac{1}{2}$-star-compact) space $X$ having a regular closed $G_{\delta}$-subset which is not $1\frac{1}{2}$-starcompact (hence, not $\mathcal K$-starcompact).