Extending semilattices to frames using sites and coverages

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286591" target="_blank" >RIV/00216208:11320/14:10286591 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2478/s12175-014-0223-9" target="_blank" >http://dx.doi.org/10.2478/s12175-014-0223-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2478/s12175-014-0223-9" target="_blank" >10.2478/s12175-014-0223-9</a>

Result language
angličtina
Original language name
Extending semilattices to frames using sites and coverages
Original language description
Each meet semilattice S is well known to be freely extended to a frame by its down-sets DS. In this article we present, first, the complete range of frame extensions generated by S; it turns out to be a sub-coframe of the coframe C of sublocales of DS, indeed, an interval in C, with DS as the top and the extension of S respecting all the exact joins in S as the bottom. Then, the Heyting and Boolean case is discussed; there, the bottom extension is shown to coincide with the Dedekind-MacNeille completion. The technique used is a technique of sites, generalizing that used in [JOHNSTONE, P. T.: Stone Spaces. Cambridge Stud. Adv. Math. 3, Cambridge University Press, Cambridge, 1982]. (C) 2014 Mathematical Institute Slovak Academy of Sciences
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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