TY - JOUR ID - 807 TI - $z^\circ$-filters and related ideals in $C(X)$ JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Mohamadian, Rostam AD - Shahid Chamran University of Ahvaz Y1 - 2015 PY - 2015 VL - 2 IS - 2 SP - 57 EP - 66 KW - $z^circ$-filter KW - prime $z^circ$-filter KW - ci-free $z^circ$-filter KW - i-free $z^circ$-filter KW - $z^circ$-ultrafilter KW - i-compact DO - N2 - 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. UR - https://as.yazd.ac.ir/article_807.html L1 - https://as.yazd.ac.ir/article_807_bb25ddc73dfd82df981f87a48bcc5e25.pdf ER -