Dimension Invariance Theorem
R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.
See also
Domain Invariance TheoremExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Dimension Invariance Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DimensionInvarianceTheorem.html