invariance of dimension
The following non-trivial result was proven by Brouwer [1]around 1910 [2].
Theorem (Invariance of dimension)Suppose and are open subsets of respectively .If and are non-empty and homeomorphic, then .
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 availablehttp://www.math.cornell.edu/ hatcher/AT/ATpage.htmlonline.