Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 2, Pages 65–70
The lower neighborhoods problem in a space with closure and a finitary theorem
N. G. Parvatov
Tomsk State University, Tomsk, Russia
In this paper we study conditions under which all finitely generated subsets in a space (i.e., in a set with the closure property) have finite lower neighborhoods. We prove the finitary property of such a space. In addition, we state the Birchoff and Frink finatary theorem more precisely. Considered questions have applications to discrete functional systems with superpositions.
space, closure property, closure property of finite character, completeness problem, expressibility problem, finitely generated classes, criterion system, lower neighborhood.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:2, 56–60
N. G. Parvatov, “The lower neighborhoods problem in a space with closure and a finitary theorem”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 2, 65–70; Russian Math. (Iz. VUZ), 55:2 (2011), 56–60
Citation in format AMSBIB
\paper The lower neighborhoods problem in a~space with closure and a~finitary theorem
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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