Share This Article:

Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constraints of Asymptotic Character

Full-Text HTML Download Download as PDF (Size:418KB) PP. 526-551
DOI: 10.4236/iim.2010.29062    5,636 Downloads   8,182 Views  


Abstract problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attrac- tion sets are constructed. AMS (MOS) subject classification. 46A, 49 K 40.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Chentsov, "Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constraints of Asymptotic Character," Intelligent Information Management, Vol. 2 No. 9, 2010, pp. 526-551. doi: 10.4236/iim.2010.29062.


[1] J. Warga, “Optimal Control of Differential and Functional Eguations,” Academic Press, New York, 1972.
[2] R. V. Gamkrelidze, “Foundations of Optimal Control Theory,” Izdat. Tbil. Univ., Tbilissi, Russian, 1977.
[3] N. N. Krasovskii, “The Theory of the Control of Motion,” Nauka, Moscow, Russian, 1968.
[4] R. J. Duffin, “Linear Inequalites and Related Systems,” Annals of Mathematics Studies, Vol. 38, 1956, pp. 157- 170.
[5] E. G. Gol‘stein, “Duality Theory in Mathematical Programming and Its Applications,” Nauka, Moscow, Russian, 1971.
[6] N. N. Krasovskii and A. I. Subbotin, “Game-Theoretical Control Problems,” Springer Verlag, Berlin, 1988.
[7] A. G. Chentsov, “Constructing Operations of the Limit Passage with the Emploument of Ultrafilters of Measurable Spaces,” Avtomatika i telemekhanika, Vol. 6, No. 11, 2007, pp. 208-222.
[8] A. G. Chentsov and S. I. Tarasova, “Extensions of Abstract Analog of Unstable Control Problems,” Functional Differential Equations, Vol. 16, No. 2, 2009, pp. 237-261.
[9] A. G. Chentsov, “Asymptotic Attainability,” Kluwer, Dor- drecht, 1997.
[10] K. Kuratowski and A. Mostowski, “Set Theory,” North- Holland, Amsterdam, 1967.
[11] N. Bourbaki, “General Topology,” Nauka, Moskow, Russian, 1968.
[12] J. L. Kelley, “General Topology,” Van Nostrand, Prnceton, NJ, 1957.
[13] R. Engelking, “General Topology,” PWN, Warszawa, 1977.
[14] G. Cr?tzer, “General Lattice Theory,” Akademie-Verlag, Berlin, 1978.
[15] J. Neveu, “Bases Math Matiques Du Calcul Des Probabilit s,” Masson, Paris, 1964.
[16] A. G. Chentsov and S. I. Morina, “Extensions and Rela- xations,” Kluwer Academic Publishers, Dordrecht/ Boston/London, 2002.
[17] A. G. Chentsov, “Some Constructions of Asymptotic An- alisis Connected with Stone-?ech Compactification,” Co- ntemporary Mathematics and its Applications, Vol. 26, 2004, pp. 119-150.
[18] A. G. Chentsov, “Extensions of Abstract Problems of Attainability: Nonsequential Version. Proceedings of the Steklov Institute of Mathematics,” Suppl. 2, 2007, pp. S46-S82. Pleiades Publishing, Ltd., 2007.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.