On an aspect of scatteredness in the point-free setting

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10330656" target="_blank" >RIV/00216208:11320/16:10330656 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4171/PM/1980" target="_blank" >http://dx.doi.org/10.4171/PM/1980</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/PM/1980" target="_blank" >10.4171/PM/1980</a>

Result language
angličtina
Original language name
On an aspect of scatteredness in the point-free setting
Original language description
It is well known that a locale is subfit iff each of its open sublocales is a join of closed ones, and fit iff each of its closed sublocales is a meet of open ones. This formulation, however, exaggerates the parallelism between the behavior of fitness and subfitness. For it can be shown that a locale is fit iff each of its sublocales is a meet of closed ones, but it is not the case that a locale is subfit iff each of its sublocales is a join of closed ones. Thus we are led to take up the very natural question of which locales have the feature that every sublocale is a join of closed sublocales. In this note we show that these are precisely the subfit locales which are scattered in the point-free sense of [13], and we add a variation for spatial frames.
Czech name
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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
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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
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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