Abstract:
A reachability problem with constraints of asymptotic nature is considered in a topological space. The properties of a rather general procedure that defines an extension of the problem are studied. In particular, we specify a rule that transforms an arbitrary extension scheme (a compactifier) to a similar scheme with the property that the continuous extension of the objective operator of the reachability problem is homeomorphic. We show how to use this rule in the case when the extension is realized in the ultrafilter space of a broadly understood measurable space. This version is then made more specific for the case of an objective operator defined on a nondegenerate interval of the real line.
Citation:
A. G. Chentsov, “Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 294–309; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 102–118
\Bibitem{Che16}
\by A.~G.~Chentsov
\paper Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 1
\pages 294--309
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2017
\vol 296
\issue , suppl. 1
\pages 102--118
\crossref{https://doi.org/10.1134/S0081543817020109}
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Linking options:
https://www.mathnet.ru/eng/timm1282
https://www.mathnet.ru/eng/timm/v22/i1/p294
This publication is cited in the following 14 articles:
A. G. Chentsov, “Nekotorye voprosy, svyazannye s realizatsiei mnozhestv prityazheniya s tochnostyu do napered zadannoi okrestnosti”, Vestnik rossiiskikh universitetov. Matematika, 29:147 (2024), 352–376
A. G. Chentsov, “Some Properties of Ultrafilters Related to Their Use As Generalized Elements”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S53–S68
A. G. Chentsov, “O topologicheskikh svoistvakh mnozhestva prityazheniya v prostranstve ultrafiltrov”, Vestnik rossiiskikh universitetov. Matematika, 28:143 (2023), 335–356
A. G. Chentsov, “Stseplennost semeistv mnozhestv, superkompaktnost i nekotorye obobscheniya”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 208, VINITI RAN, M., 2022, 79–90
A. G. Chentsov, A. N. Sesekin, “Relaksatsiya zadachi o dostizhimosti dlya lineinoi upravlyaemoi sistemy neitralnogo tipa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:1 (2021), 70–88
A. G. Chentsov, “Ultrafiltry i maksimalnye stseplennye sistemy”, Tr. IMM UrO RAN, 26, no. 1, 2020, 274–292
A. G. Chentsov, “Maksimalnye stseplennye sistemy i ultrafiltry: osnovnye predstavleniya i topologicheskie svoistva”, Vestnik rossiiskikh universitetov. Matematika, 25:129 (2020), 68–84
A. G. Chentsov, “Ultrafiltry kak dopustimye obobschennye elementy v usloviyakh ogranichenii asimptoticheskogo kharaktera”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:2 (2020), 312–323
A. G. Chentsov, “O superkompaktnosti prostranstva ultrafiltrov s topologiei volmenovskogo tipa”, Izv. IMI UdGU, 54 (2019), 74–101
A. G. Chentsov, “Some properties of ultrafilters of widely understood measurable spaces”, Dokl. Math., 99:3 (2019), 255–259
A. G. Chentsov, E. G. Pytkeev, “Constraints of asymptotic nature and attainability problems”, Vestn. Udmurt. Univ.-Mat. Mekh. Kompyuternye Nauk., 29:4 (2019), 569–582
E. G. Pytkeev, A. G. Chentsov, “Volmenovskii kompaktifikator i ego primenenie dlya issledovaniya abstraktnoi zadachi o dostizhimosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 199–212
A. G. Chentsov, “Maximal linked systems and ultrafilters in abstract attainability problem”, IFAC-PapersOnLine, 51:32 (2018), 239–244
A. G. Chentsov, “Superrasshirenie kak bitopologicheskoe prostranstvo”, Izv. IMI UdGU, 49 (2017), 55–79
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