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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 1, Pages 113–142 (Mi vuu212)  

This article is cited in 30 scientific papers (total in 30 papers)

MATHEMATICS

Filters and ultrafilters in the constructions of attraction sets

A. G. Chentsov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: The abstract attainability problem with constraints of asymptotic character is considered; for this problem, the nonsequential (generally speaking) attraction set obtained by the comparison to the solution an attraction element is constructed. Self solutions are defined as nets, filters, or ultrafilters of the space of usual solutions (each of the above-mentioned classes is sufficient for constructing of attraction set). Main attention are given to questions of constructing of attraction sets in the class of measurable spaces interpreted very broad (spaces with the families closed with respect to intersections, measurable spaces with algebras of sets and so forth). The construction arising under consideration of ultrafilters of lattices of sets is used as instrument of investigation.

Keywords: attraction set, topological space, ultrafilter.

Full text: PDF file (362 kB)
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Document Type: Article
UDC: 519.6
MSC: 28A33
Received: 01.09.2010

Citation: A. G. Chentsov, “Filters and ultrafilters in the constructions of attraction sets”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 1, 113–142

Citation in format AMSBIB
\Bibitem{Che11}
\by A.~G.~Chentsov
\paper Filters and ultrafilters in the constructions of attraction sets
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 1
\pages 113--142
\mathnet{http://mi.mathnet.ru/vuu212}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Chentsov, “Elementy prityazheniya v abstraktnoi zadache o dostizhimosti s ogranicheniyami asimptoticheskogo kharaktera”, Vestn. Tambovsk. un-ta. Estestvennye i tekhnich. nauki, 16:4 (2011), 1213–1219  mathscinet  elib
    2. Chentsov A.G., “Ultrafilters in the constructions of attraction sets: Problem of compliance to constraints of asymptotic character”, Differ. Equ., 47:7 (2011), 1059–1076  crossref  mathscinet  zmath  isi  elib  scopus
    3. Chentsov A.G., “Generalized limits and representations of attraction sets in problems with constraints of asymptotic character”, Dokl. Math., 85:1 (2012), 83–86  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. G. Chentsov, “Representation of attraction elements in abstract attainability problems with asymptotic constraints”, Russian Math. (Iz. VUZ), 56:10 (2012), 38–49  mathnet  crossref  mathscinet
    5. A. G. Chentsov, “K voprosu o strukture mnozhestv prityazheniya v topologicheskom prostranstve”, Izv. IMI UdGU, 2012, no. 1(39), 147–150  mathnet
    6. A. G. Chentsov, “Preobrazovaniya ultrafiltrov i ikh primenenie v konstruktsiyakh mnozhestv prityazheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 85–102  mathnet
    7. A. G. Chentsov, “Yarusnye otobrazheniya i preobrazovaniya na osnove ultrafiltrov”, Tr. IMM UrO RAN, 18, no. 4, 2012, 298–314  mathnet  elib
    8. A. G. Chentsov, “Ob odnom primere postroeniya mnozhestv prityazheniya s ispolzovaniem prostranstva Stouna”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 108–124  mathnet
    9. A. G. Chentsov, “On the question of representation of ultrafilters in a product of measurable spaces”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 65–78  mathnet  crossref  mathscinet  isi  elib
    10. A. G. Chentsov, “Attraction sets in abstract attainability problems: equivalent representations and basic properties”, Russian Math. (Iz. VUZ), 57:11 (2013), 28–44  mathnet  crossref
    11. A. G. Chentsov, “On the question of representation of ultrafilters and their application in extension constructions”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 29–48  mathnet  crossref  mathscinet  isi  elib
    12. A. G. Chentsov, “On certain problems of the structure of ultrafilters related to extensions of abstract control problems”, Autom. Remote Control, 74:12 (2013), 2020–2036  mathnet  crossref  isi
    13. A. G. Chentsov, “K voprosu o predstavlenii kompaktov Stouna”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 156–174  mathnet
    14. A. G. Chentsov, “Ultrafiltry izmerimykh prostranstv i ikh primenenie v konstruktsiyakh rasshirenii”, Tr. IMM UrO RAN, 20, no. 1, 2014, 285–304  mathnet  mathscinet  elib
    15. A. G. Chentsov, “Nekotorye svoistva ultrafiltrov, svyazannye s konstruktsiyami rasshirenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 1, 87–101  mathnet
    16. 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
    17. A. G. Chentsov, Yu. V. Shapar', “On extension of the maximin problem”, Autom. Remote Control, 75:7 (2014), 1283–1300  mathnet  crossref  isi
    18. 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
    19. A. G. Chentsov, “K voprosu o soblyudenii ogranichenii v klasse obobschennykh elementov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 3, 90–109  mathnet
    20. 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
    21. A. G. Chentsov, “K voprosu o realizatsii elementov prityazheniya v abstraktnykh zadachakh o dostizhimosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:2 (2015), 212–229  mathnet  elib
    22. 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
    23. E. G. Pytkeev, A. G. Chentsov, “Nekotorye svoistva otkrytykh ultrafiltrov”, Izv. IMI UdGU, 2015, no. 2(46), 140–148  mathnet  elib
    24. A. G. Chentsov, “Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 102–118  mathnet  crossref  mathscinet  isi  elib
    25. 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
    26. E. G. Pytkeev, A. G. Chentsov, “Open ultrafilters and separability with the use of the operation of closure”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 177–190  mathnet  crossref  crossref  mathscinet  isi  elib
    27. A. G. Chentsov, “Superrasshirenie kak bitopologicheskoe prostranstvo”, Izv. IMI UdGU, 49 (2017), 55–79  mathnet  crossref  elib
    28. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy mnozhestv”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 365–388  mathnet  crossref  elib
    29. Alexander G. Chentsov, “Some representations connected with ultrafilters and maximal linked systems”, Ural Math. J., 3:2 (2017), 100–121  mathnet  crossref
    30. E. G. Pytkeev, A. G. Chentsov, “Volmenovskii kompaktifikator i ego primenenie dlya issledovaniya abstraktnoi zadachi o dostizhimosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 199–212  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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