invariance of dimension
Theorem (Invariance of dimension) Suppose $U$ and $V$ are open subsets of ${\mathbb{R}}^{n}$ respectively ${\mathbb{R}}^{m}$. If $U$ and $V$ are non-empty and homeomorphic, then $n=m$.
References
- 1 The MacTutor History of Mathematics archive, http://www-gap.dcs.st-and.ac.uk/ history/Mathematicians/Brouwer.htmlentry on Luitzen Egbertus Jan Brouwer
- 2 A. Hatcher, Algebraic Topology, Cambridge University Press, 2002. Also available http://www.math.cornell.edu/ hatcher/AT/ATpage.htmlonline.
Title | invariance of dimension |
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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 |