Zero elements and $z$-ideals in modified pointfree topology
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Abstract:
In this paper, we define and study the notion of zero elements in topoframes; a topoframe is a pair $(L, tau)$, abbreviated $L_{ tau}$, consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complemented elements in $L$. We show that the $f$-ring $ mathcal{R}(L_tau)$, the set of $tau$-real continuous functions on $L$, is uniformly complete. Also, the set of all zero elements in a topoframe is closed under the formation of countable meets and finite joins. Also, we introduce the notion of $z$-filters and $z$-ideals in modified pointfree topology and make ready some results about them.
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Journal title
volume 43 issue 7
pages 2205- 2226
publication date 2017-12-30
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