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

Abstract

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.