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