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