An inverse theorem on 'economic' maps
type: Item
instance of: scholarly article
title: An inverse theorem on 'economic' maps
zbMATH Open document ID: 1253.54029
author: S. I. Bogataya
author: E. A. Kudryavtseva
author: S. A. Bogatyi
published in: Sbornik: Mathematics
publication date: 2012-07-31T00:00:00Z
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 6062376
zbMATH Keywords: embedding
zbMATH Keywords: Euclidean space
zbMATH Keywords: dimension
MaRDI profile type: Publication
full work available at URL: sm2012v203n04abeh004234
OpenAlex ID: W2137114350
DOI: 10.1070/SM2012V203N04ABEH004234
review text: The authors deal with `economic' maps to Euclidean spaces; the quotes are apt as the notion is left mostly undefined. The reader can get an idea of what such a map might be by considering the main results of this paper; these are of the form: if \(\dim X\leq n\) then for most maps from~\(X\) to~\(\mathbb{R}^m\) and certain numbers~\(d\) the preimages of \(d\)-dimensional hyperplanes are small in some sense. Various theorems of this kind can be found in [\textit{S. A. Bogatyi} and \textit{V. M. Valov}, Sb. Math. 196, No. 11, 1585--1603 (2005); translation from Mat. Sb. 196, No. 11, 33--52 (2005; Zbl 1141.54014)]. In this paper the authors prove that certain bounds in the latter paper are sharp.
reviewed by: K. P. Hart
description: scientific article; zbMATH DE number 6062376