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Russia Yekaterinburg
Section  Mathematics 
Title  Some representations of free ultrafilters 
Author(s)  Pytkeev E.G.^{ab}, Chentsov A.G.^{ab} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a}, Ural Federal University^{b} 
Abstract  Constructions related to the representation of free $\sigma$multiplicative ultrafilters of widely interpreted measurable spaces are considered. These constructions are based on the representations connected with the application of open ultrafilters for cofinite and cocountable topologies. Such ultrafilters are preserved (as maximal filters) under the replacement of topologies by algebra and $\sigma$algebra generated by abovementioned topologies, respectively. In (general) case of cocountable topology, uniqueness of $\sigma$multiplicative free ultrafilter composed of nonempty open sets is established. It is demonstrated that the given property is preserved for $\sigma$algebras containing cocountable topology. Two topologies of the space of bounded finitely additive Borel measures with the property of uniqueness of remainder for sequentially closed set of Dirac measures under the closure construction are stated. 
Keywords  algebra of sets, measure, topology, ultrafilter 
UDC  519.6 
MSC  28A33 
DOI  10.20537/vm160305 
Received  1 July 2016 
Language  Russian 
Citation  Pytkeev E.G., Chentsov A.G. Some representations of free ultrafilters, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 345365. 
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