Results 1 to 10 of about 40 (38)
$\sigma$-locales in Formal Topology [PDF]
Logical Methods in Computer Science, 2022 A $\sigma$-frame is a poset with countable joins and finite meets in which binary meets distribute over countable joins. The aim of this paper is to show that $\sigma$-frames, actually $\sigma$-locales, can be seen as a branch of Formal Topology, that is,
Francesco Ciraulo
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Products on Maximal Compact Frames
Ratio Mathematica, 2023 In topological spaces, many topological properties such as separation properties, paracompactness etc. are preserved under the act of taking product of topological spaces.
Jayaprasad P. N.
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On the Menger and almost Menger properties in locales
Applied General Topology, 2021 The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober TD-spaces.
Tilahun Bayih +2 more
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Another proof of Banaschewski's surjection theorem [PDF]
Categories and General Algebraic Structures with Applications, 2019 We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform ...
Dharmanand Baboolal +2 more
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When spectra of lattices of $z$-ideals are Stone-Čech compactifications [PDF]
Mathematica Bohemica, 2017 Let $X$ be a completely regular Hausdorff space and, as usual, let $C(X)$ denote the ring of real-valued continuous functions on $X$. The lattice of $z$-ideals of $C(X)$ has been shown by Martínez and Zenk (2005) to be a frame.
Themba Dube
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Localic maps constructed from open and closed parts [PDF]
Categories and General Algebraic Structures with Applications, 2017 Assembling a localic map f:L→M from localic maps fi:Si→M, i∈J, defined on closed resp. open sublocales (J finite in the closed case) follows the same rules as in the classical case.
Ales Pultr, Jorge Picado
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A little more on ideals associated with sublocales [PDF]
Categories and General Algebraic Structures with ApplicationsAs usual, let $\mathcal RL$ denote the ring of real-valued continuous functions on a completely regular frame $L$. Let $\beta L$ and $\lambda L$ denote the Stone-\v{C}ech compactification of $L$ and the Lindel\"of coreflection of $L$, respectively ...
Oghenetega Ighedo +2 more
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A note on weakly pseudocompact locales
Applied General Topology, 2017 We revisit weak pseudocompactness in pointfree topology, and show that a locale is weakly pseudocompact if and only if it is Gδ-dense in some compactification.
Themba Dube
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Injective locales over perfect embeddings and algebras of the upper powerlocale monad
Applied General Topology, 2003 We show that the locales which are injective over perfect sublocale embeddings coincide with the underlying objects of the algebras of the upper powerlocale monad, and we characterize them as those whose frames of opens enjoy a property analogous to ...
Martín Escardó
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Notes on the spatial part of a frame [PDF]
Categories and General Algebraic Structures with ApplicationsA locale (frame) L has a largest spatial sublocale generated by the primes (spectrum points), the spatial part SpL. In this paper we discuss some of the properties of the embeddings SpL ⊆ L.
Igor Arrieta, Jorge Picado, Ales Pultr
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