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Название: On the supercompactness of ultrafilter space with the topology of Wallman type
Авторы: Chentsov, A. G.
Дата публикации: 2019
Издатель: Udmurt State University
Библиографическое описание: Chentsov, A. G. On the supercompactness of ultrafilter space with the topology of Wallman type / A. G. Chentsov. — DOI 10.20537/2226-3594-2019-54-07 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2019. — Iss. 54. — P. 74-101.
Аннотация: This paper is concerned with ultrafilters and maximal linked systems of widely understood measurable spaces (nonempty sets with π-systems of its subsets are meant). The sets of ultrafilters and maximal linked systems are transformed to bitopological spaces by applying constructions that (in idea) meet the Wallman and Stone schemes. The focus is on ultrafilter space with topology of Wallman type. Conditions on the initial π-system for which the given space is supercompact are specified. Concrete classes of (widely understood) measurable spaces are listed for which the above-mentioned conditions are realized. Special attention is also given to one abstract problem of attainability under conditions when the choice of a concrete solution may have the following uncertainty: the set defining constraints can be an arbitrary element of a given nonempty family. The question of the existence of universally realized (in limit) elements in the space of values of the goal operator in our problem is considered. To obtain sufficient solutions, the supercompactness property of the ultrafilter space for special measurable structure is used; this structure is sufficient (under corresponding suppositions) for realization of all variants of constraints on the choice of a usual solution (control). © 2019 А. Г. Ченцов.
Ключевые слова: MAXIMAL LINKED SYSTEM
TOPOLOGY
ULTRAFILTER
URI: http://hdl.handle.net/10995/90073
https://elar.urfu.ru/handle/10995/90073
Условия доступа: info:eu-repo/semantics/openAccess
Идентификатор РИНЦ: 41435143
Идентификатор SCOPUS: 85079134759
Идентификатор WOS: 000512131100007
Идентификатор PURE: 11456496
ISSN: 2226-3594
DOI: 10.20537/2226-3594-2019-54-07
Сведения о поддержке: Russian Foundation for Basic Research, RFBR: 18–01–00410
Funding. The research was funded by the Russian Foundation for Basic Research, project number 18–01–00410.
Располагается в коллекциях:Научные публикации, проиндексированные в SCOPUS и WoS CC

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