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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 4, Pages 289–307 (Mi timm1022)  
This article is cited in 6 scientific papers (total in 6 papers)

On the question of representation of ultrafilters and their application in extension constructions

A. G. Chentsovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (270 kB) Citations (6)
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Abstract: We study ultrafilters of widely understood measurable spaces and possibilities of their application as generalized elements in the construction of attraction sets in abstract attainability problems with constraints of asymptotic nature. A class of measurable spaces is specified for which all ultrafilters including free ultrafilters (with empty intersection of all of its sets) are built constructively.
Keywords: measurable space, attraction set, ultrafilter.
Received: 12.04.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 287, Issue 1, Pages 29–48
DOI: https://doi.org/10.1134/S0081543814090041
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: A. G. Chentsov, “On the question of representation of ultrafilters and their application in extension constructions”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 289–307; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 29–48
Citation in format AMSBIB
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\vol 19
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\pages 289--307
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages 29--48
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Linking options:
  • https://www.mathnet.ru/eng/timm1022
  • https://www.mathnet.ru/eng/timm/v19/i4/p289
    • This publication is cited in the following 6 articles:
    1. Alexander G. Chentsov, “Products of ultrafilters and maximal linked systems on widely understood measurable spaces”, Ural Math. J., 7:2 (2021), 3–32  mathnet  crossref  mathscinet
    2. A. G. Chentsov, A. P. Baklanov, I. I. Savenkov, “Zadacha o dostizhimosti s ogranicheniyami asimptoticheskogo kharaktera”, Izv. IMI UdGU, 2016, no. 1(47), 54–118  mathnet  mathscinet  zmath  elib
    3. A. G. Chentsov, A. P. Baklanov, “On an asymptotic analysis problem related to the construction of an attainability domain”, Proc. Steklov Inst. Math., 291 (2015), 279–298  mathnet  crossref  crossref  isi  elib
    4. E. G. Pytkeev, A. G. Chentsov, “On the structure of ultrafilters and properties related to convergence in topological spaces”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 164–181  mathnet  crossref  mathscinet  isi  elib
    5. A. G. Chentsov, A. P. Baklanov, “On the question of construction of an attraction set under constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 40–55  mathnet  crossref  isi  elib
    6. A. G. Chentsov, E. G. Pytkeev, “Some topological structures of extensions of abstract reachability problems”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 36–54  mathnet  crossref  mathscinet  isi  elib
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