\(K\)-subanalytic rectilinearization and uniformization
type: Item
instance of: scholarly article
title: \(K\)-subanalytic rectilinearization and uniformization
zbMATH Open document ID: 1038.32010
DOI: 10.2478/BF02475178
published in: Central European Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
review text: 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 \(x\to | x| ^\lambda,\) \( x\in\mathbb R^n,\) \(\lambda\in\mathbb R\).
Mathematics Subject Classification ID: 32B20
Mathematics Subject Classification ID: 14P15
Mathematics Subject Classification ID: 32B05
zbMATH DE Number: 2028881
zbMATH Keywords: K-subanalytic sets
zbMATH Keywords: rectilinearization
zbMATH Keywords: uniformization
author: Artur Piękosz
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.2478/bf02475178
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description: scientific article; zbMATH DE number 2028881