Ultrafilters as admissible generalized elements under asymptotic constraints

Abstract

The problem of compliance with constraints of asymptotic nature (CAN) and its expansion in the class of ultrafilters (u/f) of widely understood measurable space are considered. The representation of a set of admissible generalized elements as an attraction set (AS) corresponding to the given system of CAN is investigated. In particular, the question about non-emptiness of the given AS under very general suppositions with respect to measurable structure for which corresponding u/f are defined, is investigated. The above-mentioned measurable structure is defined as a π-system with “zero” and “unit” (π-system is a nonempty family of sets closed with respect to finite intersections). The u/f family is equipped with topology of Wallman type. © 2020 Udmurt State University. All rights reserved.