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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 2, Pages 250–267 (Mi timm1075)  
This article is cited in 4 scientific papers (total in 4 papers)

On the structure of ultrafilters and properties related to convergence in topological spaces

E. G. Pytkeevab, A. G. Chentsovba

a B. N. Yeltsin Ural Federal University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (257 kB) Citations (4)
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Abstract: We consider properties of broadly understood measurable spaces that provide the preservation of maximality when ultrafilters are restricted to filters of the corresponding subspace. We study conditions that guarantee the convergence of images of ultrafilters consisting of open sets under continuous mappings.
Keywords: filter base, measurable space, topology, ultrafilter.
Received: 10.12.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 289, Issue 1, Pages 164–181
DOI: https://doi.org/10.1134/S0081543815050156
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: E. G. Pytkeev, A. G. Chentsov, “On the structure of ultrafilters and properties related to convergence in topological spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 2, 2014, 250–267; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 164–181
Citation in format AMSBIB
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\paper On the structure of ultrafilters and properties related to convergence in topological spaces
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\pages 250--267
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages 164--181
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Linking options:
  • https://www.mathnet.ru/eng/timm1075
  • https://www.mathnet.ru/eng/timm/v20/i2/p250
    • This publication is cited in the following 4 articles:
    1. A. G. Chentsov, “O superkompaktnosti prostranstva ultrafiltrov s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 54 (2019), 74–101  mathnet  crossref  elib
    2. 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
    3. E. G. Pytkeev, A. G. Chentsov, “Nekotorye svoistva otkrytykh ultrafiltrov”, Izv. IMI UdGU, 2015, no. 2(46), 140–148  mathnet  elib
    4. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:87
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