ON THE Sλ(X) AND λ-ZERO DIMENSIONAL SPACES

Let Sλ(X) = f C(X) : X Z(f) λ, such that λ is a regular cardinal number with λ X. It is generalization of CF(X) = Sℵ0 (X) and SCF(X) = Sℵ1 (X). Using this concept we extend some of the basic results concerning the socle to Sλ(X). It is shown that if X is a λ-pseudo discrete space, then CK,λ(X) Sλ(X). Sλ-completely regular spaces are investigated. Consequently, X is a Sℵ1-completely regular space if and only if X is 1-zero dimensional space. SλP-spaces are introduced and studied.