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invariance of dimension
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(Theorem)
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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 $\sR^n$ respectively $\sR^m$ . If $U$ and $V$ are non-empty and homeomorphic, then $n=m$ .
- 1
- The MacTutor History of Mathematics archive, entry on Luitzen Egbertus Jan Brouwer
- 2
- A. Hatcher, Algebraic Topology, Cambridge University Press, 2002. Also available online.
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"invariance of dimension" is owned by Koro. [ owner history (1) ]
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Cross-references: homeomorphic, open subsets, theorem
There are 4 references to this entry.
This is version 4 of invariance of dimension, born on 2003-06-24, modified 2003-12-20.
Object id is 4390, canonical name is InvarianceOfDimension.
Accessed 2904 times total.
Classification:
| AMS MSC: | 55-00 (Algebraic topology :: General reference works ) |
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Pending Errata and Addenda
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