Michael Byers, International Law and the Arctic (Cambridge: Cambridge Studies in International and Comparative law, Cambridge University Press, 2013)

Johnstone, Rachael Lorna

doi:10.33112/nm.9.1.22

Cited by 38 publications

(65 citation statements)

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“…A frame homomorphism between algebraic frames is called a coherent map if it maps compact elements to compact elements. The usage of the same adjective "coherent" for frames and homomorphisms is purely historical (see [10,Notes to Chapter II]).…”

Section: Algebraic Framesmentioning

confidence: 99%

First steps going down on algebraic frames

Dube¹

2018

HJMS

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We extend the ring-theoretic concept of going down to algebraic frames and coherent maps. We then use the notion introduced to characterize algebraic frames of dimension 0 and frames of dimension at most 1. An application to rings yields a characterization of von Neumann regular rings that appears to have hitherto been overlooked. Namely, a commutative ring A with identity is von Neumann regular if and only if Ann(I) + P = A, for every prime ideal P of A and any finitely generated ideal I of A contained in P .

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Section: Algebraic Framesmentioning

confidence: 99%

First steps going down on algebraic frames

Dube¹

2018

HJMS

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“…Similarly, a co-frame has pseudosupplements, i.e., co-pseudocomplements a # tx | x a 1u. For more about frames see, e.g., [13,17], or the more recent [15]. with intersection for meet, and join defined by Exact meets and joins have various motivations.…”

Section: 2mentioning

confidence: 99%

Notes on Exact Meets and Joins

Ball

Picado

Pultr

2013

Appl Categor Struct

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An exact meet in a lattice is a special type of infimum characterized by, inter alia, distributing over finite joins. In frames, the requirement that a meet is preserved by all frame homomorphisms makes for a slightly stronger property. In this paper these concepts are studied systematically, starting with general lattices and proceeding through general frames to spatial ones, and finally to an important phenomenon in Scott topologies.

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“…A topological space X is sober if each irreducible closed subset of X is the closure of exactly one point in X. Moreover, sobriety of topological spaces can be described via the Papert-Papert-Isbell adjunction O pt (see [7,14]) between the category Top of topological spaces and the category Loc of locales (see [8]). More precisely, a topological space X is sober if η X : X −→ pt(O(X)) is a bijection, where η X denotes the unit of the above adjunction.…”

Section: Introductionmentioning

confidence: 99%

Bounded sobriety and k-bounded sobriety of Q-cotopological spaces

Zhang

Wang

2019

Filomat

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In this paper, we extend bounded sobriety and k-bounded sobriety to the setting of Q-cotopological spaces, where Q is a commutative and integral quantale. The main results are: (1) The category BSobQ-CTop of all bounded sober Q-cotopological spaces is a full reflective subcategory of the category SQ-CTop of all stratified Q-cotopological spaces; (2) We present the relationships among Hausdorff, T 1 , sobriety, bounded sobriety and k-bounded sobriety in the setting of Q-cotopological spaces; (3) For a linearly ordered quantale Q, a topological space X is bounded (resp., k-bounded) sober if and only if the corresponding Q-cotopological space ω Q (X) is bounded (resp., k-bounded) sober, where ω Q : Top −→ SQ-CTop is the well-known Lowen functor in fuzzy topology.

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Michael Byers, International Law and the Arctic (Cambridge: Cambridge Studies in International and Comparative law, Cambridge University Press, 2013)

Abstract: International Law in the Arctic is a most welcome text to scholars and teachers of Arctic studies that to date has no close competitor.

Cited by 38 publications

References 0 publications

First steps going down on algebraic frames

First steps going down on algebraic frames

Notes on Exact Meets and Joins

Bounded sobriety and k-bounded sobriety of Q-cotopological spaces

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