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.

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.

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.

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.

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.