Results 11 to 20 of about 355 (91)
Overlap Algebras: a Constructive Look at Complete Boolean Algebras [PDF]
, 2020 The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set.
Ciraulo, Francesco, Contente, Michele
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Overlap Algebras as Almost Discrete Locales [PDF]
, 2016 Boolean locales are almost discrete. In fact, spatial Boolean locales are the same thing as discrete spaces. This does not make sense intuitionistically, since (non-trivial) discrete locales fail to be Boolean.
Ciraulo, Francesco
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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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On locales whose countably compact sublocales have compact closure [PDF]
, 2023 summary:Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called ${\rm cl}$-isocompact spaces. They have been considered in T. Dube, I. Naidoo, C.
Dube, Themba
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Positivity relations on a locale [PDF]
, 2016 This paper analyses the notion of a positivity relationof Formal Topology from the point of view of the theory of Locales. It is shown that a positivity relation on a locale corresponds to a suitable class of points of its lower powerlocale.
Ciraulo, Francesco, Vickers, Steven
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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
doaj +1 more source
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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Rings of real functions in pointfree topology [PDF]
, 2011 This paper deals with the algebra F(L) of real functions on a frame L and its subclasses LSC(L) and USC(L) of, respectively, lower and upper semicontinuous real functions. It is well known that F(L) is a lattice-ordered ring; this paper presents explicit
Davenport, E. +7 more
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Adjoint maps between implicative semilattices and continuity of localic maps [PDF]
, 2022 We study residuated homomorphisms (r-morphisms) and their adjoints, the so-called localizations (or l-morphisms), between implicative semilattices, because these objects may be characterized as semilattices whose unary meet operations have adjoints ...
Erné, Marcel +2 more
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