Complexities and representations of F-Borel spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401075" target="_blank" >RIV/00216208:11320/19:10401075 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21230/19:00337954
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=VaY54Lsinq" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=VaY54Lsinq</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/dm794-2-2019" target="_blank" >10.4064/dm794-2-2019</a>
Alternative languages
Result language
angličtina
Original language name
Complexities and representations of F-Borel spaces
Original language description
We investigate the F-Borel complexity of topological spaces in their different compactifications. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications. We also develop a theory of representations of F-Borel sets, and show how to apply this theory to prove that the complexity of hereditarily Lindelof spaces is absolute (that is, the same in every compactification). We use these representations to characterize the complexities attainable by a specific class of topological spaces. This provides an alternative proof of the first result, and implies the existence of a space with non-absolute additive complexity. We discuss the method used by Talagrand to construct the first example of a space with non-absolute complexity, hopefully providing an explanation which is more accessible than the original one. We also discuss the relation between complexity and local complexity, and show how to construct amalgamation-like compactifications.
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
Result was created during the realization of more than one project. More information in the Projects tab.
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
Dissertationes Mathematicae
ISSN
0012-3862
e-ISSN
—
Volume of the periodical
540
Issue of the periodical within the volume
540
Country of publishing house
PL - POLAND
Number of pages
69
Pages from-to
1-69
UT code for WoS article
000476629800001
EID of the result in the Scopus database
2-s2.0-85069843567