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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 Sciences^{a}, Ural Federal University^{b} 
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. 365388. 
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