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Russia Yekaterinburg
Section Mathematics
Title Ultrafilters and maximal linked systems
Author(-s) Chentsov A.G.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
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.
Keywords lattice of sets, topology, ultrafilter
UDC 519.6
MSC 28A33
DOI 10.20537/vm170307
Received 5 July 2017
Language Russian
Citation Chentsov A.G. Ultrafilters and maximal linked systems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 365-388.
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