Results 21 to 30 of about 141 (99)
Locatedness and overt sublocales [PDF]
Annals of Pure and Applied Logic, 2010 Locatedness is one of the fundamental notions in constructive mathematics. The existence of a positivity predicate on a locale, i.e. the locale being overt, or open, has proved to be fundamental in constructive locale theory. We show that the two notions are intimately connected. Bishop defines a metric space to be compact if it is complete and totally
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C-connected frame congruences [PDF]
Categories and General Algebraic Structures with Applications, 2017 We discuss the congruences θ that are connected as elements of the (totally disconnected) congruence frame \CFL, and show that they are in a one-to-one correspondence with the completely prime elements of L, giving an explicit formula.
Dharmanand Baboolal +2 more
doaj +1 more source
Immunological Reviews, Volume 329, Issue 1, January 2025.ABSTRACT αβT cells protect vertebrates against many diseases, optimizing surveillance using mechanical force to distinguish between pathophysiologic cellular alterations and normal self‐constituents. The multi‐subunit αβT‐cell receptor (TCR) operates outside of thermal equilibrium, harvesting energy via physical forces generated by T‐cell motility and ...
Robert J. Mallis +19 more
wiley +1 more source
Sublocale-based ideals of rings of integer-valued functions
, 2021 Let L be a zero-dimensional frame and ZL be the ring of continuous integer-valued functions on L. We associate with each sublocale of L, the Banaschewski compacti cation of L, an ideal of ZL, and study the behaviour of these types of ideals.
Tlharesakgosi, Batsile
core
Axiom $T_D$ and the Simmons sublocale theorem [PDF]
, 2019 summary:More precisely, we are analyzing some of H. Simmons, S.\,B. Niefield and K.\,I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the ...
Picado, Jorge, Pultr, Aleš
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Bulletin of the Belgian Mathematical Society - Simon Stevin, 2010 As \textit{P.\,T.\,Johnstone} stressed in [``The art of pointless thinking: a student's guide to the category of locales'', Res. Expo. Math. 18, 85--107 (1991; Zbl 0745.18003)], ``one of the most important reasons for studying the category of locales as a substitute for (and in many ways an improvement on) the category of topological spaces'' (which ...
Lu, Tao, He, Wei, Wang, Xijuan
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Remainders in pointfree topology
, 2018 Remainders of subspaces are important e.g. in the realm of compactifications. Their extension to pointfree topology faces a difficulty: sublocale lattices are more complicated than their topological counterparts (complete atomic Boolean algebras ...
Picado, Jorge +2 more
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Open sublocales of localic completions
Journal of Logic and Analysis, 2010 We give a constructive characterization of morphisms between open sublocales of localic completions of locally compact metric (LCM) spaces, in terms of continuous functions. The category of open subspaces of LCM spaces is thereby shown to embed fully faithfully into the category of locales (or formal topologies).
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On the categorical behaviour of locales and D-localic maps
, 2022 It was shown by Banaschewski and Pultr that the classical adjunction between Top and Loc restricts to an adjunction between the category TopD of TD-spaces and their continuous maps, and the category LocD of all locales and localic maps which preserve ...
Gutiérrez García, Francisco Javier +1 more
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General insertion and extension theorems for localic real functions
, 2011 In this paper we investigate localic real functions on frames. We provide a necessary and sufficient condition for the insertion of a continuous localic real function between two arbitrary comparable localic real functions.
Tomasz Kubiak +3 more
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