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Article
Uniform Approximation of Homeomorphisms by Diffeomorphisms
Topology and its Applications (2014)
  • Stefan Müller, University of Illinois at Urbana-Champaign
Abstract
We prove that a compactly supported homeomorphism of a smooth manifold of dimension n≥5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given homeomorphism is in addition volume preserving, then it can also be approximated uniformly by volume preserving diffeomorphisms.
Keywords
  • Uniform approximation,
  • Homeomorphism,
  • Diffeomorphism,
  • Isotopic,
  • Volume preserving
Disciplines
Publication Date
December, 2014
DOI
10.1016/j.topol.2014.10.003
Publisher Statement
This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the authors must hold the rights or the work must be under Creative Commons Attribution licenseCreative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Topology and its Applications
Citation Information
Stefan Müller. "Uniform Approximation of Homeomorphisms by Diffeomorphisms" Topology and its Applications Vol. 178 (2014) p. 315 - 319
source:http://arxiv.org/abs/0901.1002
doi:10.1016/j.topol.2014.10.003
Available at: http://works.bepress.com/stefan-muller/3/