The Kuratowski convergence and connected components

被引：10

作者：

Denkowska, Zofia ^{[1
]}

Denkowski, Maciej P. ^{[2
]}

机构：

[1] Univ Angers, Dept Math, LAREMA, CNRS,UMR 6093, F-49045 Angers 1, France

[2] Univ Bourgogne, Inst Math Bourgogne, CNRS, UMR 5584, F-21078 Dijon, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 387卷 / 01期

关键词：

Tame geometry; Subanalytic sets; Kuratowski convergence; ANALYTIC SETS;

D O I：

10.1016/j.jmaa.2011.08.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：48 / 65

页数：18

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