Maximal Linked Systems and Ultrafilters in Abstract Attainability Problem

Abstract

The given investigation is oriented to study of generalized elements (GE) for solving problems of attainability under constraints of asymptotic character. But, the development of this direction required a special study of the issues connected with structure of the GE themselves. In considered problems, GE are used for extension of the space of usual solutions or usual controls. This extension has an analogy with extension of topological spaces (TS). So, we use compactification procedures. It is important to know the possibilities for realization of the corresponding compactification of the initial solution space. This investigation is directed at this work. We consider topological constructions realized by ultrafilters of widely understood measurable spaces. © 2018