The lower neighborhoods problem in a space with closure and a finitary theorem

N. G. Parvatov

Tomsk State University, Tomsk, Russia

Abstract: 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.

Keywords: space, closure property, closure property of finite character, completeness problem, expressibility problem, finitely generated classes, criterion system, lower neighborhood.

UDC: 519.716

Received: 24.06.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:2, 56–60

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