零轨迹的次解析丛和管状邻域
Subanalytic Bundles and Tubular Neighbourhoods of Zero-Loci
摘要：
我们引入了实解析流形$M$的子解析子集$X$上的子解析丛（具有有限维向量空间$P$的截面）的自然和相当一般的概念，并证明了当$M$是紧的时，在$P$中存在Baire截面子集$U$，其零轨迹在$X$中具有管状邻域，同胚于给定丛对这些零轨迹的限制.
英文摘要：
We introduce the natural and fairly general notion of a subanalytic bundle (with a finite dimensional vector space $P$ of sections) on a subanalytic subset $X$ of a real analytic manifold $M$, and prove that when $M$ is compact, there is a Baire subset $U$ of sections in $P$ whose zero-loci in $X$ have tubular neighbourhoods, homeomorphic to the restriction of the given bundle to these zero-loci.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
