%0 Journal Article %T $z^\circ$-filters and related ideals in $C(X)$ %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Mohamadian, Rostam %D 2015 %\ 11/01/2015 %V 2 %N 2 %P 57-66 %! $z^\circ$-filters and related ideals in $C(X)$ %K $z^circ$-filter %K prime $z^circ$-filter %K ci-free $z^circ$-filter %K i-free $z^circ$-filter %K $z^circ$-ultrafilter %K i-compact %R %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. %U https://as.yazd.ac.ir/article_807_bb25ddc73dfd82df981f87a48bcc5e25.pdf