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Russia Yekaterinburg
Year
2012
Issue
3
Pages
85-102
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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 Sciencesa
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. 85-102.
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