Zc-EMBEDDED SUBSETS OF A TOPOLOGICAL SPACE

The ring Cc(X) as a subring of the ring C(X) consists of all continuous functions with countable image. Also, the space Min(Cc(X)), the space of minimal prime ideals of Cc(X) with Zariski topology, as a subspace of Spec(Cc(X)) is zero-dimensional but not necessarily a basically disconnected and compact space. We consider some relations between the topological properties of Min(Cc(X)) and the spece X. In this article we introduce zc-embedded of a topological space, Oc z-spaces and countably cozero complemented spaces. Furthermore, by these spaces we obtain some conditions in which Min(Cc(X)) becomes a compact and basically disconnected space.