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

نویسنده

چکیده مقاله:

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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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 ...

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عنوان ژورنال

دوره 2  شماره 2

صفحات  57- 66

تاریخ انتشار 2015-11-01

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