Closure and connected component of a planar global semianalytic set defined by analytic functions definable in o-minimal structure

被引：0

作者：

Fujita, Masato ^{[1
]}

机构：

[1] Japan Coast Guard Acad, Dept Liberal Arts, 5-1 Wakaba Cho, Kure, Hiroshima 7378512, Japan

来源：

ARCHIV DER MATHEMATIK | 2017年 / 109卷 / 06期

关键词：

o-minimal structure; Global semianalytic set; SUBANALYTIC SETS; FIELD;

D O I：

10.1007/s00013-017-1107-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a global semianalytic set defined by real analytic functions definable in an o-minimal structure. When the o-minimal structure is polynomially bounded, we show that the closure of this set is a global semianalytic set defined by definable real analytic functions. We also demonstrate that a connected component of a planar global semianalytic set defined by real analytic functions definable in a substructure of the restricted analytic field is a global semianalytic set defined by definable real analytic functions.

引用

页码：529 / 538

页数：10

共 3 条

[1] Closure and connected component of a planar global semianalytic set defined by analytic functions definable in o-minimal structure
Masato Fujita
Archiv der Mathematik, 2017, 109 : 529 - 538
[2] Algebraic approximation of analytic sets definable in an o-minimal structure
Bilski, Marcin
Rusek, Kamil
ANNALES POLONICI MATHEMATICI, 2010, 97 (02) : 185 - 200
[3] MICHAEL'S SELECTION THEOREM FOR A MAPPING DEFINABLE IN AN O-MINIMAL STRUCTURE DEFINED ON A SET OF DIMENSION 1
Czapla, Malgorzata
Pawlucki, Wieslaw
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2017, 49 (01) : 377 - 380

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