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

TL;DR

This paper explores the use of filters and ultrafilters to find approximate solutions in attainability problems within topological spaces, introducing new methods for constructing attraction sets.

Contribution

It introduces a nonsequential approach using filters and ultrafilters for attainability problems, expanding the theoretical framework.

Findings

Developed a nonsequential version of Warga approximate solutions.

Constructed attraction sets using filters and ultrafilters.

Extended the attainability problem analysis in topological spaces.

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. Attraction sets are constructed.