Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102686
Full metadata record
DC FieldValueLanguage
dc.contributor.authorChentsov, A. G.en
dc.date.accessioned2021-08-31T15:04:45Z-
dc.date.available2021-08-31T15:04:45Z-
dc.date.issued2020-
dc.identifier.citationChentsov A. G. On certain analogues of linkedness and supercompactness / A. G. Chentsov. — DOI 10.35634/2226-3594-2020-55-08 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2020. — Vol. 55. — P. 113-134.en
dc.identifier.issn22263594-
dc.identifier.otherFinal2
dc.identifier.otherAll Open Access, Bronze3
dc.identifier.otherhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85093909978&doi=10.35634%2f2226-3594-2020-55-08&partnerID=40&md5=3c3ecc149e7fd9381c9447063ae837be
dc.identifier.urihttp://hdl.handle.net/10995/102686-
dc.description.abstractNatural generalizations of properties of the family linkedness and the topological space supercompactness are considered. We keep in mind reinforced linkedness when nonemptyness of intersection of preassigned number of sets from a family is postulated. Analogously, supercompactness is modified: it is postulated the existence of an open subbasis for which, from every covering (by sets of the subbasis), it is possible to extract a subcovering with a given number of sets (more precisely, not more than a given number). It is clear that among all families having the reinforced linkedness, one can distinguish families that are maximal in ordering by inclusion. Under natural and (essentially) “minimal” conditions imposed on the original measurable structure, among the mentioned maximal families with reinforced linkedness, ultrafilters are certainly contained. These ultrafilters form subspaces in the sense of natural topologies corresponding conceptually to schemes of Wallman and Stone. In addition, maximal families with reinforced linkedness, when applying topology of the Wallman type, have the above-mentioned property generalizing supercompactness. Thus, an analogue of the superextension of the T1-space is realized. The comparability of “Wallman” and “Stone” topologies is established. As a result, bitopological spaces (BTS) are realized; for these BTS, under equipping with analogous topologies, ultrafilter sets are subspaces. It is indicated that some cases exist when the above-mentioned BTS is nondegenerate in the sense of the distinction for forming topologies. At that time, in the case of “usual” linkedness (this is a particular case of reinforced linkedness), very general classes of spaces are known for which the mentioned BTS are degenerate (the cases when origial set, i. e., “unit” is equipped with an algebra of sets or a topology). © 2020 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. All rights reserved.en
dc.description.sponsorshipThe research was supported by the Russian Foundation for Basic Research (project no. 18–01– 00410).en
dc.format.mimetypeapplication/pdfen
dc.language.isoruen
dc.publisherUdmurt State Universityen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceIzv. Inst. Mat. Inform. Udmurt. Gos. Univ.2
dc.sourceIzvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universitetaen
dc.subjectMAXIMAL LINKED SYSTEMen
dc.subjectSUPERCOMPACTNESSen
dc.subjectTOPOLOGYen
dc.subjectULTRAFILTERen
dc.titleOn certain analogues of linkedness and supercompactnessen
dc.titleО некоторых аналогах сцепленности и суперкомпактностиru
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.doi10.35634/2226-3594-2020-55-08-
dc.identifier.scopus85093909978-
local.contributor.employeeChentsov, A.G., N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russian Federation, Ural Federal University, Ul. Mira, 19, Yekaterinburg, 620002, Russian Federation
local.description.firstpage113-
local.description.lastpage134-
local.volume55-
local.contributor.departmentN. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russian Federation
local.contributor.departmentUral Federal University, Ul. Mira, 19, Yekaterinburg, 620002, Russian Federation
local.identifier.pure13200369-
local.identifier.eid2-s2.0-85093909978-
local.fund.rffi18-01-00410-
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

Files in This Item:
File Description SizeFormat 
2-s2.0-85093909978.pdf276,91 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.