PlanetMath: invariance of dimension

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invariance of dimension

(Theorem)

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

Theorem (Invariance of dimension) Suppose and are open subsets of $\mathbb{R}^n$ respectively $\mathbb{R}^m$ . If and are non-empty and homeomorphic, then .

References

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.

"invariance of dimension" is owned by Koro. [ owner history (1) ]

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Attachments:: proof of invariance of dimension (Proof) by Algeboy

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Cross-references: homeomorphic, open subsets
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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 2193 times total.

Classification:

AMS MSC:

55-00 (Algebraic topology :: General reference works )

Pending Errata and Addenda

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