Subanalytic Bundles and Tubular Neighbourhoods of Zero-Loci

Original · EN

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.