Geodesic
Ultrafilters as admissible generalized elements under asymptotic constraints
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 2, pp. 312-323

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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.
Keywords: attraction set, topological space, ultrafilter. 
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     author = {A. G. Chentsov},
     title = {Ultrafilters as admissible generalized elements under asymptotic constraints},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {312--323},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2020_30_2_a11/}
}
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A. G. Chentsov. Ultrafilters as admissible generalized elements under asymptotic constraints. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 2, pp. 312-323. http://geodesic.mathdoc.fr/item/VUU_2020_30_2_a11/