Definable one-dimensional topologies in O-minimal structures

被引：1
|
作者：
Peterzil, Ya'acov [1 ]
Rosel, Ayala [1 ]
机构：
[1] Univ Haifa, Dept Math, Haifa, Israel
来源：
ARCHIVE FOR MATHEMATICAL LOGIC | 2020年 / 59卷 / 1-2期
关键词：
o-minimality; Definable topology; One-dimensional topology;
D O I：
10.1007/s00153-019-00680-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space ( X, tau) is definably homeomorphic to an affine definable space (namely, a definable subset of Mn with the induced subspace topology). One of the main results says that it is sufficient for X to be regular and decompose into finitely many definably connected components.
引用
收藏
页码：103 / 125
页数：23
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