\(K\)-subanalytic rectilinearization and uniformization (Q1419662)

In the theory of subanalytic sets the two theorems: the uniformization theorem (each closed subanalytic set in a real analytic manifold is the image of a real analytic manifold by a proper real analytic map) and the rectilinearization theorem (a theorem on a local representation of subanalytic sets in a real analytic manifold as a finite union of images of ``quadrants'' in \(\mathbb R^n\)) are basic in the study of properties of subanalytic sets. The author generalizes these two theorems to a broader class of sets, \(K\)-subanalytic sets. They are defined analougosly to the subanalytic sets by using not only real analytic functions (as in the case of ordinary subanalytic sets) but additionally their compositions with the functions \(x\to | x| ^\lambda,\) \( x\in\mathbb R^n,\) \(\lambda\in\mathbb R\).