Abstract:
Issues of the structure of spaces of ultrafilters and maximal linked systems are studied. We consider a widely understood measurable space (a π-system with zero and one) defined as follows: we fix a nonempty family of subsets of a given set closed under finite intersections and containing the set itself ("one") and the nonempty set ("zero"). Ultrafilters (maximal filters) and maximal linked systems are constructed on this space. Each of the obtained spaces is equipped with a pair of comparable topologies. The resulting bitopological spaces turn out to be consistent in the following sense: each space of ultrafilters is a subspace of the corresponding space of maximal linked systems. Moreover, the space of maximal linked systems with Wallman-type topology is supercompact and, in particular, compact. Possible variants of the π-systems are lattices, semialgebras and algebras of sets, topologies, and families of closed sets of topological spaces.
\Bibitem{Che18}
\by A.~G.~Chentsov
\paper Bitopological spaces of ultrafilters and maximal linked systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 1
\pages 257--272
\mathnet{http://mi.mathnet.ru/timm1513}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-1-257-272}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3782952}
\elib{https://elibrary.ru/item.asp?id=32604062}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 305
\issue , suppl. 1
\pages S24--S39
\crossref{https://doi.org/10.1134/S0081543819040059}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000436169800022}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85073537654}
Linking options:
https://www.mathnet.ru/eng/timm1513
https://www.mathnet.ru/eng/timm/v24/i1/p257
This publication is cited in the following 20 articles:
A. G. Chentsov, “Nekotorye voprosy, svyazannye s realizatsiei mnozhestv prityazheniya s tochnostyu do napered zadannoi okrestnosti”, Vestnik rossiiskikh universitetov. Matematika, 29:147 (2024), 352–376
A. G. Chentsov, “O topologicheskikh svoistvakh mnozhestva prityazheniya v prostranstve ultrafiltrov”, Vestnik rossiiskikh universitetov. Matematika, 28:143 (2023), 335–356
A. G. Chentsov, “Stseplennost semeistv mnozhestv, superkompaktnost i nekotorye obobscheniya”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 208, VINITI RAN, M., 2022, 79–90
A. G. Chentsov, “Maksimalnye stseplennye sistemy na semeistvakh izmerimykh pryamougolnikov”, Vestnik rossiiskikh universitetov. Matematika, 26:133 (2021), 77–104
A. G. Chentsov, “Maksimalnye stseplennye sistemy na proizvedeniyakh shiroko ponimaemykh izmerimykh prostranstv”, Vestnik rossiiskikh universitetov. Matematika, 26:134 (2021), 182–215
Alexander G. Chentsov, “Products of ultrafilters and maximal linked systems on widely understood measurable spaces”, Ural Math. J., 7:2 (2021), 3–32
A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy”, Tr. IMM UrO RAN, 26, no. 1, 2020, 274–292
A. G. Chentsov, “O nekotorykh analogakh stseplennosti i superkompaktnosti”, Izv. IMI UdGU, 55 (2020), 113–134
A. G. Chentsov, “Maksimalnye stseplennye sistemy i ultrafiltry: osnovnye predstavleniya i topologicheskie svoistva”, Vestnik rossiiskikh universitetov. Matematika, 25:129 (2020), 68–84
A. G. Chentsov, “Filtry i stseplennye semeistva mnozhestv”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:3 (2020), 444–467
A. G. Chentsov, “To question on some generalizations of properties of cohesion of families of sets and supercompactness of topological spaces”, Russian Math. (Iz. VUZ), 64:11 (2020), 58–72
A. G. Chentsov, “Nekotorye topologicheskie svoistva prostranstva maksimalnykh stseplennykh sistem s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 56 (2020), 122–137
A. G. Chentsov, “Superkompaktnye prostranstva ultrafiltrov i maksimalnykh stseplennykh sistem”, Tr. IMM UrO RAN, 25, no. 2, 2019, 240–257
Alexander G. Chentsov, “To a question on the supercompactness of ultrafilter spaces”, Ural Math. J., 5:1 (2019), 31–47
A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye sootnosheniya”, Izv. IMI UdGU, 53 (2019), 138–157
A. G. Chentsov, “O superkompaktnosti prostranstva ultrafiltrov s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 54 (2019), 74–101
A. G. Chentsov, “Some properties of ultrafilters of widely understood measurable spaces”, Dokl. Math., 99:3 (2019), 255–259
A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye svoistva i topologicheskie konstruktsii”, Izv. IMI UdGU, 52 (2018), 86–102
Chentsov A.G., “Maximal Linked Systems and Ultrafilters in Abstract Attainability Problem”, IFAC PAPERSONLINE, 51:32 (2018), 239–244
A. G. Chentsov, “Maksimalnye stseplennye sistemy i ultrafiltry shiroko ponimaemykh izmerimykh prostranstv”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:124 (2018), 846–860
Citation in format AMSBIB
Contact us: