Geodesic
Filters and ultrafilters in the constructions of attraction sets
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 113-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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The abstract attainability problem with constraints of asymptotic character is considered; for this problem, the nonsequential (generally speaking) attraction set obtained by the comparison to the solution an attraction element is constructed. Self solutions are defined as nets, filters, or ultrafilters of the space of usual solutions (each of the above-mentioned classes is sufficient for constructing of attraction set). Main attention are given to questions of constructing of attraction sets in the class of measurable spaces interpreted very broad (spaces with the families closed with respect to intersections, measurable spaces with algebras of sets and so forth). The construction arising under consideration of ultrafilters of lattices of sets is used as instrument of investigation.
Keywords: attraction set, topological space, ultrafilter. 
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A. G. Chentsov. Filters and ultrafilters in the constructions of attraction sets. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 113-142. http://geodesic.mathdoc.fr/item/VUU_2011_1_a11/

[1] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp. | MR

[2] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968, 475 pp. | MR

[3] Chentsov A. G., “Predstavlenie maksimina v igrovoi zadache s ogranicheniyami asimptoticheskogo kharaktera”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 3, 104–119

[4] Chentsov A. G., Asymptotic attainability, Kluwer Academic Publishers, Dordrecht–Boston–London, 1997, 322 pp. | MR | Zbl

[5] Chentsov A. G., Morina S. I., Extensions and Relaxations, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002, 408 pp. | MR | Zbl

[6] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970, 416 pp. | MR

[7] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969, 309 pp. | MR | Zbl

[8] Burbaki N., Obschaya topologiya, Nauka, M., 1968, 272 pp. | MR

[9] Engelking R., Obschaya topologiya, Mir, M., 1986, 751 pp. | MR

[10] Kelli Dzh. L., Obschaya topologiya, Nauka, M., 1981, 431 pp. | MR

[11] Grettser G., Obschaya teoriya reshetok, Mir, M., 1982, 452 pp. | MR

[12] Chentsov A. G., “Nesekventsialnye priblizhennye resheniya v abstraktnykh zadachakh o dostizhimosti”, Trudy Instituta matematiki i mekhaniki UrO RAN, 12, no. 1, Ekaterinburg, 2006, 216–241 | MR | Zbl

[13] Arkhangelskii A V., “Kompaktnost”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 50, 1989, 5–128 | MR | Zbl

[14] Aleksandryan R. A., Mirzakhanyan E. A., Obschaya topologiya, Vysshaya shkola, M., 1979, 336 pp. | Zbl

[15] Chentsov A. G., Elementy konechno-additivnoi teorii mery, v. II, UGTU-UPI, Ekaterinburg, 2010, 541 pp.

[16] Chentsov A. G., “Nekotorye konstruktsii asimptoticheskogo analiza, svyazannye s kompaktifikatsiei Stouna–Chekha”, Sovremennaya matematika i ee prilozheniya, 26, Akademiya nauk Gruzii, Institut kibernetiki, 2005, 119–150 | MR

[17] Chentsov A. G., Finitely additive measures and relaxations of extremal problems, Plenum Publishing Corporation, New York–London–Moscow, 1996, 244 pp. | MR | Zbl

[18] Optimal Control, Contemporary Mathematics and its Applications, 17, 2004, 3–153 | DOI | MR | Zbl

[19] Chentsov A. G., “Rasshireniya abstraktnykh zadach o dostizhimosti: nesekventsialnaya versiya”, Trudy Instituta matematiki i mekhaniki UrO RAN, 13, no. 2, 2007, 184–217

[20] Bell M. G., “Compact ccc non-separable spaces of small weight”, Topology Proceedings, 5 (1980), 11–25 | MR

[21] Bastrykov E. S., “O nekotorykh tochkakh rasshireniya Bella schetnogo diskretnogo prostranstva”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 4, 3–6

[22] Gryzlov A. A., Bastrykov E. S., Golovastov R. A., “O tochkakh odnogo bikompaktnogo rasshireniya $N$”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 3, 10–17