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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 2, Pages 65–70 (Mi ivm7234)  
The lower neighborhoods problem in a space with closure and a finitary theorem

N. G. Parvatov

Tomsk State University, Tomsk, Russia
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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.
Received: 24.06.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 2, Pages 56–60
DOI: https://doi.org/10.3103/S1066369X11020071
Bibliographic databases:
Document Type: Article
UDC: 519.716
Language: Russian
Citation: 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
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\paper The lower neighborhoods problem in a~space with closure and a~finitary theorem
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 2
\pages 65--70
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 2
\pages 56--60
\crossref{https://doi.org/10.3103/S1066369X11020071}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953022652}
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