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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 3, Pages 365–388 (Mi vuu595)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Ultrafilters and maximal linked systems

A. G. Chentsovab

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620002, Russia
b Institute of Radioelectronics and Information Technologies, Ural Federal University, ul. Mira, 32, Yekaterinburg, 620002, Russia

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.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations


DOI: https://doi.org/10.20537/vm170307

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Document Type: Article
UDC: 519.6
MSC: 28A33
Received: 05.07.2017

Citation: A. G. Chentsov, “Ultrafilters and maximal linked systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017), 365–388

Citation in format AMSBIB
\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{http://elibrary.ru/item.asp?id=30267248}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alexander G. Chentsov, “Some representations connected with ultrafilters and maximal linked systems”, Ural Math. J., 3:2 (2017), 100–121  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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