On the locally socle of C(X) whose local cozeroset is cocountable (cofinite)

Abstract

Let $C_F(X)$ be the socle of $C(X)$ (i.e., the sum of minimal ideals of $C(X)$). We introduce and study the concept of colocally socle of $C(X)$ as $C_{mu}{S_{lambda}}(X)=left{ fin C(X):|Xbackslash {S}^{lambda}_{f}|