Results 81 to 90 of about 141 (99)
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T D property and spatial sublocales
Acta Mathematica Sinica, 1995Summary: As one of main backgrounds of locale theory, topologies have close connections with locales. But locales have other backgrounds such as algebra, mathematical logic, etc. So there are many differences between locales and topologies. Spatiality is an important localic property to investigate the connections between locales and topologies.
Liu, Yingming, Luo, Maokang
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Scatteredness: Joins of Closed Sublocales
2021The property to be discussed in this chapter is very restrictive, so restrictive that one may hesitate to think about it as of an honest separation axiom (similarly like one does not usually think of discreteness as of a separation property: it says that distinct points can be separated by closed sets, but this is really somehow going too far).
Jorge Picado, Aleš Pultr
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2011
Let X be a (T0-)space and let \( A {\subseteq} X \) be a subspace. We have the embedding \( jA : A {\subseteq} X \) and the sublocale homomorphism (i.e., frame quotient) \( {\Omega}(jA) = (U {\mapsto} U {\cap} A) : {\Omega}(X) \rightarrow {\Omega}(A) \).
Jorge Picado, Aleš Pultr
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Let X be a (T0-)space and let \( A {\subseteq} X \) be a subspace. We have the embedding \( jA : A {\subseteq} X \) and the sublocale homomorphism (i.e., frame quotient) \( {\Omega}(jA) = (U {\mapsto} U {\cap} A) : {\Omega}(X) \rightarrow {\Omega}(A) \).
Jorge Picado, Aleš Pultr
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Continuous extensions of real functions on arbitrary sublocales and C-, C⁎-, and z-embeddings
Journal of Pure and Applied Algebra, 2021The sublocale lattices are much more complicated than their topological counterparts (complete atomic Boolean algebras). Some of the main differences are that (i) each locale has a smallest dense sublocale, (ii) only complemented sublocales (most sublocales are not complemented) distribute over all covers, and (iii) covers are not necessarily stable ...
Avilez, Ana Belén, Picado, Jorge
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On ideals of rings of continuous functions associated with sublocales
Topology and its Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dube, Themba, Stephen, Dorca Nyamusi
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Locales whose coz-complemented cozero sublocales have open closures
Algebra universalis, 2020In the paper under review, the authors study the pointfree counterpart of cloz-spaces, a class of spaces introduced by \textit{M. Henriksen} et al. [Diss. Math. 280, 31 p. (1989; Zbl 0719.54033)]. A cozero sublocale \(C\) of a completely regular locale \(L\) is \textit{coz-complemented} if there is a cozero sublocale \(D\) of \(L\) such that \(C\wedge ...
Ighedo, Oghenetega, Mugochi, Martin M.
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Hewitt’s irresolvability and induced Sublocales in spatial frames
Quaestiones Mathematicae, 2019Sublocales of frames, even those representing subspaces (induced sublo-cales), are typically not complemented in the lattice of all sublocales.
Dharmanand Baboolal +3 more
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On classes of localic maps defined by their behavior on zero sublocales
Topology and its Applications, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Frame presentations of compact hedgehogs and their properties
Quaestiones Mathematicae, 2023Igor Arrieta +2 more
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