Abstract:
The family of maximal linked systems all elements of which are sets of an arbitrary lattice with “zero” and “unit” is considered; its subfamily composed of ultrafilters of that lattice is also considered. Relations between natural topologies used to equip the set of maximal linked systems and the set of the lattice ultrafilters are investigated. It is demonstrated that the last set under natural (for ultrafilter spaces) equipment is a subspace of the space of maximal linked systems under equipment with two comparable topologies one of which is similar to the topology used for the Wallman extension and the second corresponds (conceptually) to the scheme of Stone space in the case when the initial lattice is an algebra of sets. Properties of the resulting bitopological structure are detailed for the cases when our lattice is an algebra of sets, a topology, and a family of closed sets in a topological space.
\Bibitem{Che17}
\by A.~G.~Chentsov
\paper Ultrafilters and maximal linked systems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 3
\pages 365--388
\mathnet{http://mi.mathnet.ru/vuu595}
\crossref{https://doi.org/10.20537/vm170307}
\elib{https://elibrary.ru/item.asp?id=30267248}
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https://www.mathnet.ru/eng/vuu595
https://www.mathnet.ru/eng/vuu/v27/i3/p365
This publication is cited in the following 18 articles:
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, “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, “Superkompaktnye prostranstva ultrafiltrov i maksimalnykh stseplennykh sistem”, Tr. IMM UrO RAN, 25, no. 2, 2019, 240–257
A. G. Chentsov, “Bitopological spaces of ultrafilters and maximal linked systems”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S24–S39
A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy: osnovnye svoistva i topologicheskie konstruktsii”, Izv. IMI UdGU, 52 (2018), 86–102
A. G. Chentsov, “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
Alexander G. Chentsov, “Some representations connected with ultrafilters and maximal linked systems”, Ural Math. J., 3:2 (2017), 100–121
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