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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, Volume 30, Issue 2, Pages 312–323
DOI: https://doi.org/10.35634/vm200212 (Mi vuu727) 		 
MATHEMATICS

Ultrafilters as admissible generalized elements under asymptotic constraints

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/vm200212
Abstract: The problem of compliance with constraints of asymptotic nature (CAN) and its expansion in the class of ultrafilters (u/f) of widely understood measurable space are considered. The representation of a set of admissible generalized elements as an attraction set (AS) corresponding to the given system of CAN is investigated. In particular, the question about non-emptiness of the given AS under very general suppositions with respect to measurable structure for which corresponding u/f are defined, is investigated. The above-mentioned measurable structure is defined as a $\pi$-system with “zero” and “unit” ($\pi$-system is a nonempty family of sets closed with respect to finite intersections). The u/f family is equipped with topology of Wallman type.
Keywords: attraction set, topological space, ultrafilter.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00410_а
The research was supported by the Russian Foundation for Basic Research (project no. 18-01-00410).
Received: 28.02.2020
Bibliographic databases:
Document Type: Article
UDC: 519.6
MSC: 05A05, 97N70, 97N80
Language: Russian
Citation: A. G. Chentsov, “Ultrafilters as admissible generalized elements under asymptotic constraints”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:2 (2020), 312–323
Citation in format AMSBIB
\Bibitem{Che20}
\by A.~G.~Chentsov
\paper Ultrafilters as admissible generalized elements under asymptotic constraints
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 2
\pages 312--323
\mathnet{http://mi.mathnet.ru/vuu727}
\crossref{https://doi.org/10.35634/vm200212}
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    		Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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