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Applied Categorical Structures, 1994
First is shown that if \({\mathcal B}\) is an epireflective subcategory of all locales, and \({\mathcal B}\) is generated by a nice locale \(B\), then every \(A\in {\mathcal B}\) containing \(B\) as a retract is an Isbell locale (i.e., it is a regular cogenerator for a certain subcategory).
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First is shown that if \({\mathcal B}\) is an epireflective subcategory of all locales, and \({\mathcal B}\) is generated by a nice locale \(B\), then every \(A\in {\mathcal B}\) containing \(B\) as a retract is an Isbell locale (i.e., it is a regular cogenerator for a certain subcategory).
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Information Sciences, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali Kandil +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali Kandil +2 more
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Hybrid Logics of Separation Axioms
Journal of Logic, Language and Information, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2013
The classical (point-set) topology concerns points and relationships between points and subsets. Omitting points and considering only the structure of open sets leads to the notion of frames, that is, a complete lattice satisfying the dis- tributive law b ∧ A = {b ∧ a | a ∈ A}, the crucial concept of point-free topology.
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The classical (point-set) topology concerns points and relationships between points and subsets. Omitting points and considering only the structure of open sets leads to the notion of frames, that is, a complete lattice satisfying the dis- tributive law b ∧ A = {b ∧ a | a ∈ A}, the crucial concept of point-free topology.
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Complete Regularity as a Separation Axiom
Canadian Journal of Mathematics, 1969Although the axiom of complete regularity ought to be a separation axiom, in none of its usual forms does it look like an intrinsic separation axiom. Our aim in this paper is to establish such characterizations of complete regularity which naturally fit in between regularity and normality and which already have proved to be fundamental and useful. This
de Groot, J., Aarts, J. M.
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2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), 2011
We introduce a new type of separation axioms, which is called fuzzy δ-separation axioms by using the concept of fuzzy δ-open sets. Also we investigate the relation between the separation property and the subspaces. We show that fuzzy δ-separation axioms are hereditary in fuzzy regular open subspaces.
Seok Jong Lee, Sang Min Yun
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We introduce a new type of separation axioms, which is called fuzzy δ-separation axioms by using the concept of fuzzy δ-open sets. Also we investigate the relation between the separation property and the subspaces. We show that fuzzy δ-separation axioms are hereditary in fuzzy regular open subspaces.
Seok Jong Lee, Sang Min Yun
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Separation principles and the axiom of determinateness
Journal of Symbolic Logic, 1978Let Γ be a class of subsets of Baire space (ωω) closed under inverse images by continuous functions. We say such a Γ is continuously closed. Let , the class dual to Γ, consist of the complements relative to ωω of members of Γ. If Γ is not selfdual, i.e., , then let .
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The Priestley Separation Axiom for Scattered Spaces
Order, 2002The authors give a new characterization of scattered compact Hausdorff spaces. Main results: (1) Let \(X\) be a scattered compact Hausdorff space with a quasi-order \(R\). Then \(R\) is closed if and only if \((X,R)\) is a Priestley space. (2) Let \(X\) be a non-scattered compact Hausdorff space. Then there is a closed equivalence relation \(E\) on \(X\
Guram Bezhanishvili +2 more
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Separation Axioms and Direct Limits
Canadian Mathematical Bulletin, 1969A topological space X is called a direct limit of a family (Xα) of subspaces of X if and only if(1)(2)If X is a direct limit of an increasing sequence (Xn) of closed subspaces then it is well known and easy to prove that X is a T1-space resp. a T4-space provided all Xn are T1-spaces resp. T4-spaces.
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