Tightness relative to some (co)reflections in topology
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10330658" target="_blank" >RIV/00216208:11320/16:10330658 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2989/16073606.2015.1073191" target="_blank" >http://dx.doi.org/10.2989/16073606.2015.1073191</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2989/16073606.2015.1073191" target="_blank" >10.2989/16073606.2015.1073191</a>
Alternative languages
Result language
angličtina
Original language name
Tightness relative to some (co)reflections in topology
Original language description
We address what might be termed the reverse reflection problem: given a monoreflection from a category A onto a subcategory B, when is a given object B is an element of B the reflection of a proper subobject? We start with a well known specific instance of this problem, namely thefact that a compact metric space is never the Cech-Stone compactification of a proper subspace. We show that this holds also in the pointfree setting, i.e., tint a compact met rizable locale is never the (cell-Stone compactification of a proper sublocale. This is a stronger result than the classical one, but not because of an increase in scope; after all, assuming weak choice principles, every compact regular locale is the topology of a compact Ilausdorff space. The increased strength derives from the conclusion, for in general a space has many more sublocales than subspaces. We then extend the analysis from metric locales to the broader class of perfectly normal locales, i.e., those whose frame of open sets consists entirely of cozero elements. We include a second proof of these results which is purely algebraic in character. At the opposite extreme from these results, we show that an extremally disconnected locale is a compacHlication of each of its dense sublocales. Finally, we analyse the same phenomena, also in the pointiree setting, for the O-dimensional compact reflection arid for the Lindelof reflection.
Czech name
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Czech description
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Classification
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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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
2016
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
39
Issue of the periodical within the volume
3
Country of publishing house
ZA - SOUTH AFRICA
Number of pages
16
Pages from-to
421-436
UT code for WoS article
000377899400010
EID of the result in the Scopus database
2-s2.0-84949814580