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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 3, Pages 85–102 (Mi vuu339)  

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

MATHEMATICS

The transformation of ultrafilters and their application in constructions of attraction sets

A. G. Chentsov

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

Abstract: Ultrafilters of widely interpreted measurable spaces (including the spaces with semialgebras and algebras of sets) are considered. The transformation having the sense of ultrafilter extension with semialgebra of sets onto algebra generated by this semialgebra is investigated. It is established that given transformation is a homeomorphism in the sense of the natural equipments of ultrafilter spaces realizing standard compactums (in the case of measurable spaces with algebra of sets, the space of Stone representation is realized). Questions connected with representation of attraction sets in abstract attainability problem with constraints of asymptotic character are investigated. These questions are connected with the compactifications in the class of ultrafilters of measurable spaces with semialgebras of sets and some analogs for ultrafilters of $\pi$-systems.

Keywords: attraction set, constraints of asymptotic character, ultrafilter.

Full text: PDF file (260 kB)
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UDC: 517.972.8
MSC: 28A33
Received: 15.08.2011

Citation: A. G. Chentsov, “The transformation of ultrafilters and their application in constructions of attraction sets”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 3, 85–102

Citation in format AMSBIB
\Bibitem{Che12}
\by A.~G.~Chentsov
\paper The transformation of ultrafilters and their application in constructions of attraction sets
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 3
\pages 85--102
\mathnet{http://mi.mathnet.ru/vuu339}


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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, “Nekotorye svoistva ultrafiltrov, svyazannye s konstruktsiyami rasshirenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 1, 87–101  mathnet
    2. A. G. Chentsov, “O superkompaktnosti prostranstva ultrafiltrov s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 54 (2019), 74–101  mathnet  crossref
    3. A. G. Chentsov, “Superkompaktnye prostranstva ultrafiltrov i maksimalnykh stseplennykh sistem”, Tr. IMM UrO RAN, 25, no. 2, 2019, 240–257  mathnet  crossref  elib
    4. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy”, Tr. IMM UrO RAN, 26, no. 1, 2020, 274–292  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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