Yazd University Algebraic Structures and Their Applications 2382-9761 2 2 2015 11 01 $z^\circ$-filters and related ideals in $C(X)$ 57 66 807 EN Rostam Mohamadian Shahid Chamran University of Ahvaz 0000-0003-3350-366X Journal Article 2016 03 07 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. https://as.yazd.ac.ir/article_807_bb25ddc73dfd82df981f87a48bcc5e25.pdf