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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2017, Volume 49, Pages 55–79
DOI: https://doi.org/10.20537/2226-3594-2017-49-03
(Mi iimi339)
 

This article is cited in 11 scientific papers (total in 11 papers)

Superextension as bitopological space

A. G. Chentsovab

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul.S.Kovalevskoi,16, Yekaterinburg, 620990, Russia
b Institute of Radioelectronics and Information Technologies, Ural Federal University, ul.Mira,32, Yekaterinburg, 620002, Russia
References:
Abstract: Supercompact space of maximal linked systems of topological space (superextension) and its subspace consisting of ultrafilters of the family of closed sets are considered. Some relations connecting above-mentioned spaces and some corollaries relating to Wallman extension in the case of $T_1$-space are obtained. For this case, some representations of sets in the space of generalized elements (defined as closed ultrafilters) for an abstract attainability problem under constraints of asymptotic character are considered. A more general variant of the above-mentioned relations for arbitrary initial topological space is also investigated (construction that uses closed ultrafilters of initial topological space is considered). Along with equipment with topology of Wallman type, topology similar to one applied for Stone compactum is used. As a result, bitopological space of maximal linked systems and corresponding bitopological space of closed ultrafilters as its subspace are realized.
Keywords: bitopological space, closed ultrafilter, supercompactness, superextension.
Received: 30.10.2016
Bibliographic databases:
Document Type: Article
UDC: 517.977, 519.837.3
Language: Russian
Citation: A. G. Chentsov, “Superextension as bitopological space”, Izv. IMI UdGU, 49 (2017), 55–79
Citation in format AMSBIB
\Bibitem{Che17}
\by A.~G.~Chentsov
\paper Superextension as bitopological space
\jour Izv. IMI UdGU
\yr 2017
\vol 49
\pages 55--79
\mathnet{http://mi.mathnet.ru/iimi339}
\crossref{https://doi.org/10.20537/2226-3594-2017-49-03}
\elib{https://elibrary.ru/item.asp?id=29357383}
Linking options:
  • https://www.mathnet.ru/eng/iimi339
  • https://www.mathnet.ru/eng/iimi/v49/p55
  • This publication is cited in the following articles:
    1. 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
    2. A. G. Chentsov, “Bitopological spaces of ultrafilters and maximal linked systems”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S24–S39  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye svoistva i topologicheskie konstruktsii”, Izv. IMI UdGU, 52 (2018), 86–102  mathnet  crossref  elib
    4. A. G. Chentsov, “Maksimalnye stseplennye sistemy i ultrafiltry shiroko ponimaemykh izmerimykh prostranstv”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:124 (2018), 846–860  mathnet  crossref  elib
    5. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye sootnosheniya”, Izv. IMI UdGU, 53 (2019), 138–157  mathnet  crossref  elib
    6. A. G. Chentsov, “O superkompaktnosti prostranstva ultrafiltrov s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 54 (2019), 74–101  mathnet  crossref  elib
    7. A. G. Chentsov, “Superkompaktnye prostranstva ultrafiltrov i maksimalnykh stseplennykh sistem”, Tr. IMM UrO RAN, 25, no. 2, 2019, 240–257  mathnet  crossref  elib
    8. A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy”, Tr. IMM UrO RAN, 26, no. 1, 2020, 274–292  mathnet  crossref  elib
    9. A. G. Chentsov, “O nekotorykh analogakh stseplennosti i superkompaktnosti”, Izv. IMI UdGU, 55 (2020), 113–134  mathnet  crossref
    10. A. G. Chentsov, “To question on some generalizations of properties of cohesion of families of sets and supercompactness of topological spaces”, Russian Math. (Iz. VUZ), 64:11 (2020), 58–72  mathnet  crossref  crossref  isi
    11. A. G. Chentsov, “Maksimalnye stseplennye sistemy na proizvedeniyakh shiroko ponimaemykh izmerimykh prostranstv”, Vestnik rossiiskikh universitetov. Matematika, 26:134 (2021), 182–215  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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