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.