The Lower Neighborhoods Problem in a Space with Closure and a Finitary Theorem

被引：0
|
作者：
Parvatov, N. G. [1 ]
机构：
[1] Tomsk State Univ, Pr Lenina 36, Tomsk 634050, Russia
来源：
RUSSIAN MATHEMATICS | 2011年 / 55卷 / 02期
关键词：
space; closure property; closure property of finite character; completeness problem; expressibility problem; finitely generated classes; criterion system; lower neighborhood;
D O I：
10.3103/S1066369X11020071
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：56 / 60
页数：5
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