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.

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