Z°-Filters and Related Ideals in C(X)

In this article we introduce the concept of z°-filter on a topological space x. we study and investigate the behavior of z°-filters and compare them with corresponding ideals, namely, z°-ideals of c(x), the ring of real-valued continuous functions on a completely regular hausdorff space x. it is observed that x is a compact space if and only if every z°-filter is ci-fixed. finally, by using z°-ultrafilters, we prove that any arbitrary product of i-compact spaces is i-compact.