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Russia Yekaterinburg
Section  Mathematics 
Title  Some ultrafilter properties connected with extension constructions 
Author(s)  Chentsov A.G.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  General properties of ultrafilters of $\pi$systems with zero and unit used under extension constructing for abstract attainability problems with the aim of estimation for attraction sets in topological space are considered. Possibilities of employment of the abovementioned ultrafilters as general elements are considered. Among them, elements admissible with respect to constraints of asymptotic character of the initial problem are selected. Under very general conditions, the goal operator of the given problem extends to the continuous mapping that takes each ultrafilter of $\pi$system to the limit of corresponding image. The basic attraction set (an asymptotic analog of the attainability domain) is estimated from below by the continuous image of an analogous auxiliary set in the space of ultrafilters. In the particular case of realization of the Stone space (when the used $\pi$system is an algebra of sets) the abovementioned estimate is an equality connecting a desired attraction set and an auxiliary one; for the latter a sufficiently simple representation is given. The variant of application (in estimating goals) of the Wallman extension is discussed. 
Keywords  attraction set, topology, ultrafilter 
UDC  519.6 
MSC  28A33 
DOI  10.20537/vm140108 
Received  15 January 2014 
Language  Russian 
Citation  Chentsov A.G. Some ultrafilter properties connected with extension constructions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 1, pp. 87101. 
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