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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 2, Pages 289–305 (Mi timm1189)  

This article is cited in 1 scientific paper (total in 1 paper)

An abstract reachability problem: “purely asymptotic” version

A. G. Chentsovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: A reachability problem in a topological space under constraints of asymptotic nature is considered. An extension construction using elements of compactification, as well as more general procedures employing generalized elements, is studied. The primary focus is on the case where exact solutions are absent. For this case, we study conditions for the realization of the set of admissible generalized elements in a remainder appearing under the immersion of the space of ordinary solutions. In particular, we specify conditions that provide such a realization in a remainder in the case of using (as generalized elements) ultrafilters of broadly understood measurable spaces.

Keywords: attraction set, topological space, ultrafilter.

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Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 14.01.2015

Citation: A. G. Chentsov, “An abstract reachability problem: “purely asymptotic” version”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 289–305

Citation in format AMSBIB
\Bibitem{Che15}
\by A.~G.~Chentsov
\paper An abstract reachability problem: ``purely asymptotic'' version
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 2
\pages 289--305
\mathnet{http://mi.mathnet.ru/timm1189}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3408897}
\elib{http://elibrary.ru/item.asp?id=23607939}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Chentsov, “Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 102–118  mathnet  crossref  mathscinet  isi  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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