z^\circ-filters and related ideals in C(X)

In this article we introduce the concept of z^\circ-filter on a topological space X. We study and investigate the behavior of z^\circ-filters and compare them  with corresponding ideals, namely, z^\circ-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^\circ-filter is ci-fixed. Finally, by using  z^\circ-ultrafilters, we prove that any arbitrary product of i-compact spaces is i-compact.

کلیدواژه ها:

z^circ-filter ، prime z^circ-filter ، ci-free z^circ-filter ، i-free z^circ-filter ، z^circ-ultrafilter ، i-compact