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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, Volume 30, Issue 3, Pages 444–467
DOI: https://doi.org/10.35634/vm200307 (Mi vuu735) 		 
This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Filters and linked families of sets

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, 620108, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
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DOI: https://doi.org/10.35634/vm200307
Abstract: Properties of ultrafilters (u/f) and maximal linked systems (MLS) on the widely understood measurable space (MS) and representations of linked (not necessarily maximal) families and filters on this MS are investigated. Conditions realizing maximality of linked families (systems) and natural representations for bitopological spaces (BTS) of u/f and MLS are established. Equipments of sets of linked families and filters corresponding to Wallman and Stone schemes are studied; the connection of these equipments with analogous equipments (with topologies) for u/f and MLS leading to above-mentioned BTS is studied too. Properties of linked family products for two (widely understood) MS are investigated. It is shown that MLS on the $\pi$-system product (that is, on the family of «measurable» rectangles) are limited to products of corresponding MLS on initial spaces.
Keywords: maximal linked system, family of sets, topology, ultrafilter.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00410_�
The study was funded by RFBR, project number 18-01-00410.
Received: 03.08.2020
Bibliographic databases:
Document Type: Article
UDC: 519.6
MSC: 93C83
Language: Russian
Citation: A. G. Chentsov, “Filters and linked families of sets”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:3 (2020), 444–467
Citation in format AMSBIB
\Bibitem{Che20}
\by A.~G.~Chentsov
\paper Filters and linked families of sets
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 3
\pages 444--467
\mathnet{http://mi.mathnet.ru/vuu735}
\crossref{https://doi.org/10.35634/vm200307}
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