invariance of dimension
InvarianceOfDimension
2003-06-24 14:44:46
2003-12-20 05:15:44
Theorem
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The following non-trivial result was proven by Brouwer \cite{brouwer_bib}
around 1910 \cite{hatcher_at}.
{\bf Theorem\, (Invariance of dimension)}
Suppose $U$ and $V$ are open subsets of $\sR^n$ respectively $\sR^m$.
If $U$ and $V$ are non-empty and homeomorphic, then $n=m$.
\begin{thebibliography}{9}
\bibitem{brouwer_bib}
The MacTutor History of Mathematics archive, \PMlinkexternal{entry on Luitzen Egbertus Jan Brouwer}{http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brouwer.html}
\bibitem{hatcher_at} A. Hatcher, \emph{Algebraic Topology}, Cambridge University Press, 2002. Also available
\PMlinkexternal{online}{http://www.math.cornell.edu/~hatcher/AT/ATpage.html}.
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