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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 4, Pages 293–311 (Mi timm771)  

This article is cited in 23 scientific papers (total in 23 papers)

On one example of representing the ultrafilter space for an algebra of sets

A. G. Chentsovab

a Ural Federal University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Abstract problems on attainability with constraints of asymptotic nature often involve a situation when the class of sequential approximate sequence solutions (which corresponds conceptually to Vargas approach in control theory problems) is insufficient for the reproduction of effects related to the realization of limit states corresponding to the observance of asymptotic constraints. In this situation, it is necessary to use filters or nets in the original space of solutions. In the case of using filters, as easily seen, it is sufficient to take ultrafilters as analogs of Vargas approximate solutions. However, free ultrafilters, which are the most interesting form this point of view variants of ultrafilters, do not admit a constructive description. The situation can be corrected in some cases of using ultrafilters of an algebra of sets, which turns out to be acceptable in some problems of the above type. In this context, classes of measurable spaces with algebras (or, which is practically the same, with semialgebras) of sets are of interest, as they can be used to describe the set of all free ultrafilters. We analyze an example of this kind and discuss some general constructions related to representations of the space of ultrafilters.

Keywords: algebra of sets, ultrafilter.

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UDC: 517.972.8
Received: 10.01.2011

Citation: A. G. Chentsov, “On one example of representing the ultrafilter space for an algebra of sets”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 4, 2011, 293–311

Citation in format AMSBIB
\Bibitem{Che11}
\by A.~G.~Chentsov
\paper On one example of representing the ultrafilter space for an algebra of sets
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 4
\pages 293--311
\mathnet{http://mi.mathnet.ru/timm771}
\elib{http://elibrary.ru/item.asp?id=17870444}


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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, “K voprosu o strukture mnozhestv prityazheniya v topologicheskom prostranstve”, Izv. IMI UdGU, 2012, no. 1(39), 147–150  mathnet
    2. A. G. Chentsov, “Yarusnye otobrazheniya i preobrazovaniya na osnove ultrafiltrov”, Tr. IMM UrO RAN, 18, no. 4, 2012, 298–314  mathnet  elib
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. A. G. Chentsov, “K voprosu o predstavlenii kompaktov Stouna”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 156–174  mathnet
    9. 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
    10. 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
    11. 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
    12. Chentsov A.G. Baklanov A.P., “a Problem Related To Asymptotic Attainability in the Mean”, Dokl. Math., 90:3 (2014), 762–765  crossref  mathscinet  zmath  isi  elib  scopus
    13. A. G. Chentsov, “Abstraktnaya zadacha o dostizhimosti: “chisto asimptoticheskaya” versiya”, Tr. IMM UrO RAN, 21, no. 2, 2015, 289–305  mathnet  mathscinet  elib
    14. 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
    15. 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
    16. 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
    17. 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
    18. A. G. Chentsov, “Superrasshirenie kak bitopologicheskoe prostranstvo”, Izv. IMI UdGU, 49 (2017), 55–79  mathnet  crossref  elib
    19. A. G. Chentsov, I. I. Savenkov, Yu. V. Shapar, “Odna zadacha na programmnyi maksimin pri ogranicheniyakh impulsnogo kharaktera”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 91–110  mathnet  crossref  elib
    20. Chentsov A.G., “Maximal Linked Systems and Ultrafilters in Abstract Attainability Problem”, IFAC PAPERSONLINE, 51:32 (2018), 239–244  crossref  isi  scopus
    21. Alexander G. Chentsov, “To a question on the supercompactness of ultrafilter spaces”, Ural Math. J., 5:1 (2019), 31–47  mathnet  crossref  mathscinet
    22. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye sootnosheniya”, Izv. IMI UdGU, 53 (2019), 138–157  mathnet  crossref  elib
    23. A. G. Chentsov, “O superkompaktnosti prostranstva ultrafiltrov s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 54 (2019), 74–101  mathnet  crossref
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