ON THE S_{\lambda}(X) AND {\lambda}-ZERO DIMENSIONAL SPACES

Let S_\lambda(X)=\{f\in C(X) : |X\setminus Z(f)|<\lambda\}, such that \lambda is a regular cardinalnumber with \lambda\leq |X|.It is generalization of C_F (X)=S_{\aleph_۰}(X) andSC_F(X)=S_{\aleph_۱}(X). Usingthis concept we extend some of the basic results concerning the socleto S_\lambda(X). It is shown thatif X is a \lambda-pseudo discrete space, then C_{K,\lambda}(X)\subseteq S_{\lambda}(X).S_{\lambda}-completely regular spaces are investigated.Consequently, X is a S_{\aleph_۱}-completely regular space if and only if X is \aleph_۱-zero dimensional space.S_{\lambda}P-spaces are introduced and studied.

کلیدواژه ها:

lambda-super socle of C(X) ، lambda-zero dimensional space ، S_{lambda}-completely regular space ، S_{lambda}P- space