A BOOLEAN EXTENSION OF A FRAME AND A REPRESENTATION OF DISCONTINUITY
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10368624" target="_blank" >RIV/00216208:11320/17:10368624 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2989/16073606.2017.1348399" target="_blank" >http://dx.doi.org/10.2989/16073606.2017.1348399</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2989/16073606.2017.1348399" target="_blank" >10.2989/16073606.2017.1348399</a>
Alternative languages
Result language
angličtina
Original language name
A BOOLEAN EXTENSION OF A FRAME AND A REPRESENTATION OF DISCONTINUITY
Original language description
Point-free modeling of mappings that are not necessarily continuous has been so far based on the extension of a frame to its frame of sublocales, mimicking the replacement of a topological space by its discretization. This otherwise successful procedure has, however, certain disadvantages making it not quite parallel with the classical theory (see Introduction). We mend it in this paper using a certain extension S-c(L) of a frame L, which is, a.o., Boolean and idempotent. Doing this we do not lose the merits of the previous approach. In particular we show that it yields the desired results in the treatment of semicontinuity. Also, there is no obstacle to using it as a basis of a point-free theory of rings of real functions; the "ring of all real functions" F(L) = C(S-c(L)) is now order complete.
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
2017
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
40
Issue of the periodical within the volume
8
Country of publishing house
ZA - SOUTH AFRICA
Number of pages
15
Pages from-to
1111-1125
UT code for WoS article
000419972300009
EID of the result in the Scopus database
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