Geodesic
Some questions connected with implementation of attraction sets accurate to a predetermined neighborhood
Vestnik rossijskih universitetov. Matematika, Tome 29 (2024) no. 147, pp. 352-376
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Questions connected with implementation of attraction sets (AS) in attainability problem with constraints of asymptotic nature (CAN) are considered. It is investigated the possibility of AS implementation accurate to arbitrary neighborhood in class of closures of attainability sets corresponding to concrete sets from the family generating CAN. Moreover, some relations for AS generated by different CAN are considered (disjunction conditions of AS are investigated). General constructions of neighborhood implementation of AS were applied in the case when these AS were considered in the space of ultrafilters of broadly understood measurable space (MS). In particular, the case when CAN are defined by a filter was investigated in detail; for this case, under non-restrictive conditions on the original MS, the set of ultrafilters majorizing the original filter is implemented as AS. In this case (of ultrafilter space) variants of equipment of ultrafilter set with topologies of Stone and Wallman types are investigated separately.
Keywords: attraction set, constraints of asymptotic nature, neighborhood, topology 
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A. G. Chentsov. Some questions connected with implementation of attraction sets accurate to a predetermined neighborhood. Vestnik rossijskih universitetov. Matematika, Tome 29 (2024) no. 147, pp. 352-376. http://geodesic.mathdoc.fr/item/VTAMU_2024_29_147_a7/

[69] A. G. Chentsov, “About topological properties of attraction set in ultrafilter space”, Vestnik rossiyskikh universitetov. Matematika = Russian Universities Reports. Mathematics, 28:143 (2023), 335–356 (In Russian)

[70] A. G. Chentsov, A. P. Baklanov, “Ob odnoi zadache asimptoticheskogo analiza, svyazannoi s postroeniem oblasti dostizhimosti”, Optimalnoe upravlenie, Sbornik statei. K 105-letiyu so dnya rozhdeniya akademika Lva Semenovicha Pontryagina, Trudy MIAN, 291, MAIK «Nauka/Interperiodika», M., 2015, 292–311

[71] A. G. Chentsov, A. P. Baklanov, “Ob odnoi zadache, svyazannoi s asimptoticheskoi dostizhimostyu v srednem”, Doklady RAN, 459:6 (2014), 672–676 | DOI

[72] N. N. Krasovsky, Motion Control Theory, Nauka Publ., M., 1986 (In Russian)

[73] N. N. Krasovsky, Game Problems About Meeting of Movements, Nauka Publ., Moscow, 1970 (In Russian)

[74] A. I. Panasyuk, V. I. Panasyuk, Asymptotic Turnpike Optimization of Control Systems, Science and Technology Publ., Minsk, 1986 (In Russian)

[75] J. Varga, Optimal Control of Differential and Functional Equations, Nauka Publ., Moscow, 1977, 624 pp. (In Russian)

[76] A. G. Chentsov, S. I. Morina, Extensions and Relaxations, Mathematics and Its Applications, 542, Springer Dordrecht, Boston; London, 2002, 408

[77] R. V. Gamkrelidze, Fundamentals of Optimal Control, Tbilisi University Publishing House, Tbilisi, 1975, 230 (In Russian)

[78] N. N. Krasovskii, A. I. Subbotin, “Alternativa dlya igrovoi zadachi sblizheniya”, Prikladnaya matematika i mekhanika, 34:6 (1970), 1005–1022

[79] N. N. Krasovsky, A. I. Subbotin, Positional Differential Games, Nauka Publ., Moscow, 1974, 524 (In Russian)

[80] A. I. Subbotin, A. G. Chentsov, Optimization of Guarantee in Control Problems, Nauka Publ., Moscow, 1981, 288 (In Russian)

[81] A. G. Chentsov, Asymptotic Attainability, Kluwer Academic Publishers, Dordrecht–Boston–London, 1997

[82] A. G. Chentsov, Finitely Additive Measures and Relaxations of Extremal Problems, Plenum, New York, 1996, 244

[83] A. G. Chentsov, “Ultrafiltry izmerimykh prostranstv kak obobschennye resheniya v abstraktnykh zadachakh o dostizhimosti”, Tr. IMM UrO RAN, 17, 2011, 268–293

[84] A. G. Chentsov, “Filters and ultrafilters in the constructions of attraction sets”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 1, 113–142 (In Russian)

[85] K. Kuratovsky, A. Mostovsky, Set Theory, Mir Publ., Moscow, 1970 (In Russian)

[86] A. G. Chentsov, Elements of Finitely Additive Measure Theory. I, USTU-UPI, Ekaterinburg, 2008, 388 pp. (In Russian)

[87] A. V. Bulinsky, A. N. Shiryaev, Theory of Random Processes, Fizmatlit Publ., Moscow, 2005 (In Russian)

[88] J. Neve, Mathematical Foundations of Probability Theory, Mir Publ., Moscow, 1969 (In Russian)

[89] N. Bourbaki, General Topology. Basic Structures, Nauka Publ., Moscow, 1968, 279 pp. (In Russian)

[90] R. A. Alexandryan, E. A. Mirzakhanyan, General Topology, Higher School Publ., Moscow, 1979, 336 (In Russian)

[91] R. Engelking, General Topology, Mir Publ., Moscow, 1986 (In Russian)

[92] A. G. Chentsov, “Zamknutye otobrazheniya i postroenie modelei rasshireniya”, Tr. IMM UrO RAN, 29, no. 3, 2023, 274–295

[93] A. G. Chentsov, E. G. Pytkeev, “Constraints of asymptotic nature and attainability problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019), 569–582 (In Russian)

[94] A. G. Chentsov, “Kompaktifikatory v konstruktsiyakh rasshirenii zadach o dostizhimosti s ogranicheniyami asimptoticheskogo kharaktera”, Tr. IMM UrO RAN, 22, no. 1, 2016, 294–309 ; 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 | DOI

[95] A. G. Chentsov, “Ultrafilters and maximal linked systems: basic properties and topological constructions”, Izv. IMI UdGU, 52 (2018), 86–102 (In Russian)

[96] A. G. Chentsov, “Tier mappings and ultrafilter-based transformations”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 298–314 (In Russian)

[97] A. G. Chentsov, “Bitopologicheskie prostranstva ultrafiltrov i maksimalnykh stseplennykh sistem”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 257–272 ; A. G. Chentsov, “Bitopological spaces of ultrafilters and maximal linked systems”, Proc. Steklov Inst. Math. (Suppl.), 305:suppl. 1 (2019), S24–S39 | DOI

[98] A. G. Chentsov, “Some ultrafilter properties connected with extension constructions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 1, 87–101 (In Russian)

[99] A. G. Chentsov, “To question about realization of attraction elements in abstract attainability problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:2 (2015), 212–229 (In Russian)

[100] A. G. Chentsov, “On the supercompactness of ultrafilter space with the topology of Wallman type”, Izv. IMI UdGU, 54 (2019), 74–101 (In Russian)