Natural extension of EF-spaces and EZ-spaces to the pointfree context
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Jissy Nsonde Nsayi
Abstract
Two problems concerning EF-frames and EZ-frames are investigated. In [Some new classes of topological spaces and annihilator ideals, Topology Appl. 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 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.
This paper is written during my post-doctoral fellowship. The financial support is gratefully acknowledged.
(Communicated by Aleš Pultr)
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© 2019 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- Professor Anatolij DvureÄŤenskij
- A generating theorem of punctured surface triangulations with inner degree at least 4
- Natural extension of EF-spaces and EZ-spaces to the pointfree context
- On weak isometries in directed groups
- On self-injectivity of the f-ring Frm(đť“ź(â„ť), L)
- On the extensions of discrete valuations in number fields
- On certain classes of generalized derivations
- Nilpotent elements in medial semigroups
- Power of meromorphic function sharing polynomials with derivative of it’s combination with it’s shift
- Sharp coefficient bounds for starlike functions associated with the Bell numbers
- Sufficient conditions for Carathéodory functions and applications to univalent functions
- Blending type approximation by complex Szász-Durrmeyer-Chlodowsky operators in compact disks
- Linear directional differential equations in the unit ball: solutions of bounded L-index
- On oscilatory fourth order nonlinear neutral differential equations – IV
- Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms
- Lerch’s theorem on nabla time scales
-
- Convolution theorems related with the solvability of Wiener-Hopf plus Hankel integral equations and Shannon’s sampling formula
- Stabilization of third order differential equation by delay distributed feedback control with unbounded memory
- On the amenability of a class of Banach algebras with application to measure algebra
- A bivariate Kumaraswamy-exponential distribution with application
- Berry-Esseen bounds for wavelet estimator in time-varying coefficient models with censored dependent data
- Corrigendum to ”on the congruent number problem over integers of cyclic number fields”, Math. Slovaca 66(3) (2016), 561–564
Articles in the same Issue
- Regular papers
- Professor Anatolij DvureÄŤenskij
- A generating theorem of punctured surface triangulations with inner degree at least 4
- Natural extension of EF-spaces and EZ-spaces to the pointfree context
- On weak isometries in directed groups
- On self-injectivity of the f-ring Frm(đť“ź(â„ť), L)
- On the extensions of discrete valuations in number fields
- On certain classes of generalized derivations
- Nilpotent elements in medial semigroups
- Power of meromorphic function sharing polynomials with derivative of it’s combination with it’s shift
- Sharp coefficient bounds for starlike functions associated with the Bell numbers
- Sufficient conditions for Carathéodory functions and applications to univalent functions
- Blending type approximation by complex Szász-Durrmeyer-Chlodowsky operators in compact disks
- Linear directional differential equations in the unit ball: solutions of bounded L-index
- On oscilatory fourth order nonlinear neutral differential equations – IV
- Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms
- Lerch’s theorem on nabla time scales
-
- Convolution theorems related with the solvability of Wiener-Hopf plus Hankel integral equations and Shannon’s sampling formula
- Stabilization of third order differential equation by delay distributed feedback control with unbounded memory
- On the amenability of a class of Banach algebras with application to measure algebra
- A bivariate Kumaraswamy-exponential distribution with application
- Berry-Esseen bounds for wavelet estimator in time-varying coefficient models with censored dependent data
- Corrigendum to ”on the congruent number problem over integers of cyclic number fields”, Math. Slovaca 66(3) (2016), 561–564
