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Title: Ультрафильтры и максимальные сцепленные системы множеств
Other Titles: Ultrafilters and maximal linked systems
Authors: Chentsov, A. G.
Ченцов, А. Г.
Issue Date: 2017
Publisher: Udmurt State University
Удмуртский государственный университет
Citation: Ченцов А. Г. Ультрафильтры и максимальные сцепленные системы множеств / А. Г. Ченцов // Вестник Удмуртского университета. Математика. Механика. Компьютерные науки. — 2017. — Т. 27. — №. 3. — С. 365-388.
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.
Access: info:eu-repo/semantics/openAccess
RSCI ID: 30267248
SCOPUS ID: 85035766860
WOS ID: 000467760800007
PURE ID: 6165256
ISSN: 1994-9197
DOI: 10.20537/vm170307
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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