invariance of dimension

The following non-trivial result was proven by Brouwer [1] around 1910 [2].

Theorem  (Invariance of dimension) Suppose U and V are open subsets of n respectively m. If U and V are non-empty and homeomorphic, then n=m.


  • 1 The MacTutor History of Mathematics archive, history/Mathematicians/Brouwer.htmlentry on Luitzen Egbertus Jan Brouwer
  • 2 A. Hatcher, Algebraic Topology, Cambridge University Press, 2002. Also available hatcher/AT/ATpage.htmlonline.
Title invariance of dimension
Canonical name InvarianceOfDimension
Date of creation 2013-03-22 13:42:38
Last modified on 2013-03-22 13:42:38
Owner Koro (127)
Last modified by Koro (127)
Numerical id 7
Author Koro (127)
Entry type Theorem
Classification msc 55-00