2011/04/24 by Marja Kankaanrinta, Kankaanrinta, Marja
Mathematics · #14P15 #57R18 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:14P15 #msc:57R18
paper · pdf · doi:10.48550/arxiv.1104.4653
18 pages
arxiv created 2011/04/24 · arxiv updated 2011/04/26
The purpose of this paper is to define semi- and subanalytic subsets and maps in the context of real analytic orbifolds and to study their basic properties. We prove results analogous to some well-known results in the manifold case. For example, we prove that if A is a subanalytic subset of a real analytic quotient orbifold X, then there is a real analytic orbifold Y of the same dimension as A and a proper real analytic map f\colon Y→ X with f(Y)=A. We also study images and inverse images of subanalytic sets and show that if X and Y are real analytic orbifolds and if f\colon X→ Y is a subanalytic map, then the inverse image f-1(B) of any subanalytic subset B of Y is subanalytic. If, in addition, f is proper, then also the image f(A) of any subanalytic subset A of X is proper.