Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/90476
Title: | The Other Closure and Complete Sublocales | Authors: | Clementino, Maria Manuel Picado, Jorge Pultr, Aleš |
Keywords: | Frame, Locale, Frame congruence, Sublocale, Subfit frame, c-subfit frame, Fit frame, Regular frame, Fitted sublocale, Codense sublocale, Complete sublocale, Weakly complete sublocale | Issue Date: | 2018 | Publisher: | Springer | Project: | UID/MAT/00324/ 2013 | Serial title, monograph or event: | Applied Categorical Structures | Volume: | 26 | Abstract: | Sublocales of a locale (frame, generalized space) can be equivalently represented by frame congruences. In this paper we discuss, a.o., the sublocales corresponding to complete congruences, that is, to frame congruences which are closed under arbitrary meets, and present a “geometric” condition for a sublocale to be complete. To this end we make use of a certain closure operator on the coframe of sublocales that allows not only to formulate the condition but also to analyze certain weak separation properties akin to subfitness or T_1. Trivially, every open sublocale is complete. We specify a very wide class of frames, containing all the subfit ones, where there are no others. In consequence, e.g., in this class of frames, complete homomorphisms are automatically Heyting. | URI: | https://hdl.handle.net/10316/90476 | DOI: | 10.1007/s10485-018-9516-4 | Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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ClementinoPicadoPultr.pdf | 378.78 kB | Adobe PDF | View/Open |
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