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Natural extension of $EF$-spaces and $EZ$-spaces to the pointfree context

In: Mathematica Slovaca, vol. 69, no. 5
Jissy Nsonde Nsayi

Details:

Year, pages: 2019, 979 - 988
Keywords:
EF-space, EZ-space, frame, EF-frame, EZ-frame, qsz-frame, EZ-ring, Boolean algebra
About article:
Two problems concerning $EF$-frames and $EZ$-frames are investigated. In [\textit{Some new classes of topological spaces and annihilator ideals}, Topology Appl. \textbf{165} (2014), 84–97], Tahirefar defines a Tychonoff space $X$ to be an $EF$ (resp., $EZ$)-space if disjoint unions of clopen sets are completely separated (resp., every regular closed subset is the closure of a union of clopen subsets). By extending these notions to locales, we give several characterizations of $EF$ and $EZ$-frames, mostly in terms of certain ring-theoretic properties of $\mathcal{R}L$, the ring of real-valued continuous functions on $L$. We end by defining a $qsz$-frame which is a pointfree context of $qsz$-space and, give a characterization of these frames in terms of rings of real-valued continuous functions on $L$.
How to cite:
ISO 690:
Nsayi, J. 2019. Natural extension of $EF$-spaces and $EZ$-spaces to the pointfree context. In Mathematica Slovaca, vol. 69, no.5, pp. 979-988. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0282

APA:
Nsayi, J. (2019). Natural extension of $EF$-spaces and $EZ$-spaces to the pointfree context. Mathematica Slovaca, 69(5), 979-988. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0282
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 5. 10. 2019