论文标题
关于有序组的局部O-Winimal扩展的注释
Notes on definably complete locally o-minimal expansions of ordered groups
论文作者
论文摘要
我们在本文中研究了有序组的局部o最小扩展。在封闭，有限和可定义的集合上定义的可定义连续函数的表现就像在紧凑型集合上的连续函数一样。我们在封闭，有界和可定义的集合和arzela-ascoli-type定理上证明了可定义的连续函数的均匀连续性。我们提出了一个具有管状社区的特殊亚曼福尔德的概念，并表明任何可确定的集合都被分解为有限的许多具有管状邻居的特殊次曼叶。
We study definably complete locally o-minimal expansions of ordered groups in this paper. A definable continuous function defined on a closed, bounded and definable set behave like a continuous function on a compact set. We demonstrate uniform continuity of a definable continuous function on a closed, bounded and definable set and Arzela-Ascoli-type theorem. We propose a notion of special submanifolds with tubular neighborhoods and show that any definable set is decomposed into finitely many special submanifolds with tubular neighborhoods.
