Commun. Korean Math. Soc. 2003 Vol. 18, No. 4, 695-701 Printed December 1, 2003

Chang Il Kim Dankook University

Abstract : In this paper, we have characterizations of almost P-spaces which are analogous characterizations of P-spaces and we will show that if X is an almost P-space such that it is C$^*$-embedded in every almost P-space in which X is embedded, then $\mid \upsilon \text{X}-\text{X} \mid \le 1$ and that if $\mid \upsilon \text{X}-\text{X} \mid \le 1$ and $\upsilon$X is Lindel\"of, then for any almost P-space Y in which X is dense embedded, then X is C$^*$-embedded in Y.