invariance of dimension

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 $\\mathbb{R}^{n}$ 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 availablehttp://www.math.cornell.edu/ hatcher/AT/ATpage.htmlonline.

单词	InvarianceOfDimension
释义	invariance of dimension 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 $\\mathbb{R}^{n}$ 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 availablehttp://www.math.cornell.edu/ hatcher/AT/ATpage.htmlonline.
随便看	ArithmeticProgression arithmetic progression ArithmeticSeries arithmetic series Arity arity ArmstrongNumber Armstrong number AronszajnTree Aronszajn tree Arrow arrow ArrowsRelation arrows relation ArthurRubin Arthur Rubin ArtificialIntelligence artificial intelligence Artinian testing for continuity via nets TestNewcommandAndNestedLists test newcommand and nested lists TestsForLocalExtremaInLagrangeMultiplierMethod tests for local extrema in Lagrange multiplier method TestsOfDivisibilitySimpleTricks