Some aspects of (non) functoriality of natural discrete covers of locales
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404837" target="_blank" >RIV/00216208:11320/19:10404837 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Ry4zcocarU" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Ry4zcocarU</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2989/16073606.2018.1485756" target="_blank" >10.2989/16073606.2018.1485756</a>
Alternative languages
Result language
angličtina
Original language name
Some aspects of (non) functoriality of natural discrete covers of locales
Original language description
The frame S-c(L) generated by closed sublocales of a locale L is known to be a natural Boolean ("discrete") extension of a subfit L; also it is known to be its maximal essential extension. In this paper we first show that it is an essential extension of any L and that the maximal essential extensions of L and S-c(L) are isomorphic. The construction S-c is not functorial; this leads to the question of individual liftings of homomorphisms L -> M to homomorphisms S-c(L) -> S-c(M). This is trivial for Boolean L and easy for a wide class of spatial L, M . Then, we show that one can lift all h : L -> 2 for weakly Hausdorff L (and hence the spectra of L and S-c(L) are naturally isomorphic), and finally present liftings of h : L -> M for regular L and arbitrary Boolean M.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
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)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Quaestiones Mathematicae
ISSN
1607-3606
e-ISSN
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Volume of the periodical
42
Issue of the periodical within the volume
6
Country of publishing house
ZA - SOUTH AFRICA
Number of pages
15
Pages from-to
701-715
UT code for WoS article
000478889000001
EID of the result in the Scopus database
2-s2.0-85052084297