On almost discrete space

Ali Akbar Estaji

Address: Department of Mathematics, Teacher Training University Sabzevar, Iran

E-mail: aa_estaji@yahoo.com

Abstract: Let $C(X)$ be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of $C(X)$. The intersection of essential weak ideal in $C(X)$ is also studied.

AMSclassification: Primary: 54C40; Secondary: 13A30.

Keywords: essential weak ideal, weak socle, minimal ideal, almost discrete space, scattered space, Stone-Čech compactification, realcompactification