Section
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Mathematics
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Title
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Ultrafilters as admissible generalized elements under asymptotic constraints
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Author(-s)
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Chentsov A.G.ab
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Affiliations
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Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa,
Ural Federal Universityb
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Abstract
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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.
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Keywords
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attraction set, topological space, ultrafilter
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UDC
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519.6
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MSC
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05A05, 97N70, 97N80
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DOI
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10.35634/vm200212
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Received
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28 February 2020
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Language
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Russian
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Citation
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Chentsov A.G. Ultrafilters as admissible generalized elements under asymptotic constraints, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 2, pp. 312-323.
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References
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Translated under the title Obshchaya topologiya, Moscow: Nauka, 1968.
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