Results 71 to 80 of about 141 (99)
On the sublocale of an algebraic frame induced by the d-nucleus
Topology and Its Applications, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Themba Dube
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Applied Categorical Structures, 2021
\par There exists a theorem stating that given the ring \(C=C(X,\mathbb{R})\) of all continuous real-valued functions on a completely regular topological space \(X\), and its subring \(C^{*} = C^{*}(X,\mathbb{R})\) consisting of all bounded functions in \(C\), there is a one-to-one correspondence between the maximal ideals of \(C\) and those of \(C^{*}\
Themba Dube, Dorca Nyamusi Stephen
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\par There exists a theorem stating that given the ring \(C=C(X,\mathbb{R})\) of all continuous real-valued functions on a completely regular topological space \(X\), and its subring \(C^{*} = C^{*}(X,\mathbb{R})\) consisting of all bounded functions in \(C\), there is a one-to-one correspondence between the maximal ideals of \(C\) and those of \(C^{*}\
Themba Dube, Dorca Nyamusi Stephen
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Concerning P-Sublocales and Disconnectivity
Applied Categorical Structures, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Themba Dube, Dube Themba
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Insertion and extension results for pointfree complete regularity
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2013 There are insertion-type characterizations in pointfree topology that extend well known insertion theorems in point-set topology for all relevant higher separation axioms with one notable exception: complete regularity. In this paper we fill this gap. The
Javier Gutierrez Garcia, Jorge Picado
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New Aspects of Subfitness in Frames and Spaces
Applied Categorical Structures, 2016 This paper contains some new facts about subfitness and weak subfitness. In the case of spaces, subfitness is compared with the axiom of symmetry, and certain seeming discrepancies are explained.
Jorge Picado +2 more
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Quaestiones Mathematicae, 2023
We use the notion of a remote collection of a Tychonoff space to define a remote sublocale of any locale. Our definition is conservative, in the sense that, a subset is remote if and only if the sublocale it induces is remote in the locale of opens.
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We use the notion of a remote collection of a Tychonoff space to define a remote sublocale of any locale. Our definition is conservative, in the sense that, a subset is remote if and only if the sublocale it induces is remote in the locale of opens.
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Exact Filters and Joins of Closed Sublocales
Applied Categorical Structures, 2020\textit{Exact meets} in a distributive lattice are the meets \(\bigwedge a_i\) such that \((\bigwedge a_i) \vee b = \bigwedge (a_i\vee b)\) for any \(b\). This notion is due to [\textit{H. M. MacNeille}, Bull. Am. Math. Soc. 41, 193 (1935; JFM 61.0062.17)], who called them `distributive meets'.
Richard N. Ball +2 more
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On joins of complemented sublocales
Algebra universalis, 2021A sublocale of a locale \(L\) is a meet-subset \(S\) such that for all \(s \in S\) and for all \( x \in L\), the Heyting exponential \(x\rightarrow s\) belongs to \(S\). In this paper, the author deals with several aspects concerning sublocale lattices, i.e. the natural subobject lattices in the category \(\mathbf{Loc}\) of locales.
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On the relation between subspaces and sublocales
Journal of Pure and Applied Algebra, 2022In this investigation, the author shows the instrisic relation between sublocales and subspaces. This situation leads to the question: for which locales (frames) all sublocales (quotients) are spatial? In order to give a full answer, the author introduces the set of all spatial sublocales as a sublocale of the coframe of all sublocales.
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Notes on sublocales and dissolution
Quaestiones MathematicaeNo abstract.
Ales Pultr, Jorge Picado
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