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Russia Yekaterinburg
Section  Mathematics 
Title  The transformation of ultrafilters and their application in constructions of attraction sets 
Author(s)  Chentsov A.G.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  Ultrafilters of widely interpreted measurable spaces (including the spaces with semialgebras and algebras of sets) are considered. The transformation having the sense of ultrafilter extension with semialgebra of sets onto algebra generated by this semialgebra is investigated. It is established that given transformation is a homeomorphism in the sense of the natural equipments of ultrafilter spaces realizing standard compactums (in the case of measurable spaces with algebra of sets, the space of Stone representation is realized). Questions connected with representation of attraction sets in abstract attainability problem with constraints of asymptotic character are investigated. These questions are connected with the compactifications in the class of ultrafilters of measurable spaces with semialgebras of sets and some analogs for ultrafilters of $\pi$systems. 
Keywords  attraction set, constraints of asymptotic character, ultrafilter 
UDC  517.972.8 
MSC  28A33 
DOI  10.20537/vm120309 
Received  15 August 2011 
Language  Russian 
Citation  Chentsov A.G. The transformation of ultrafilters and their application in constructions of attraction sets, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 85102. 
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