RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 2, Pages 212–229 (Mi vuu478)  

This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

To question about realization of attraction elements in abstract attainability problems

A. G. Chentsov

N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: An abstract attainability problem under constraints of asymptotic character is considered; the corresponding solution is identified with an attraction set in the class of ultrafilters of the space of ordinary solutions. The remainder of the above-mentioned set with respect to closuring the set of results supplied by precise solutions is investigated (the given notion of a precise solution conceptually corresponds to Warga scheme although it is applied to the case of more general constraints). To represent the above-mentioned (basic) attraction set, the corresponding analog (of the last set) realized in the space of generalized elements is used. For thus obtained auxiliary attraction set, the remainder is analyzed; its connection with the remainder of the basic attraction set is investigated. Conditions of identifying the remainders for basic and auxiliary attraction sets are obtained. General statements are detailed for the case when generalized elements are defined in the form of ultrafilters of widely interpreted measurable spaces where free ultrafilters are responsible for the realization of remainders. It is established that, under existence of a remainder, the set of generalized admissible elements does not coincide with closuring a set of ordinary solutions (this set does not admit standard realization).

Keywords: remainder, attraction set, ultrafilter.

Full text: PDF file (302 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 519.6
MSC: 28A33
Received: 15.04.2015

Citation: A. G. Chentsov, “To question about realization of attraction elements in abstract attainability problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:2 (2015), 212–229

Citation in format AMSBIB
\Bibitem{Che15}
\by A.~G.~Chentsov
\paper To question about realization of attraction elements in abstract attainability problems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 2
\pages 212--229
\mathnet{http://mi.mathnet.ru/vuu478}
\elib{http://elibrary.ru/item.asp?id=23681103}


Linking options:
  • http://mi.mathnet.ru/eng/vuu478
  • http://mi.mathnet.ru/eng/vuu/v25/i2/p212

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. E. G. Pytkeev, A. G. Chentsov, “Nekotorye predstavleniya svobodnykh ultrafiltrov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:3 (2016), 345–365  mathnet  crossref  mathscinet  elib
    2. A. G. Chentsov, “Superrasshirenie kak bitopologicheskoe prostranstvo”, Izv. IMI UdGU, 49 (2017), 55–79  mathnet  crossref  elib
    3. 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
    4. 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  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:138
    Full text:30
    References:21

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019