Ultrafilters as admissible generalized elements under asymptotic constraints

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 $\pi$-system with “zero” and “unit” ($\pi$-system is a nonempty family of sets closed with respect to finite intersections). The u/f family is equipped with topology of Wallman type.