In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967. The result was conjectured by M. A. Lavrentev in 1938.
Theorem
Every locally homeomorphic quasiregular mapping ƒ : Rn → Rn for n ≥ 3, is a homeomorphism of Rn.
The fact that there is no such result for n = 2 is easily shown using the exponential function.
References
Zorich's theorem Wikipedia(Text) CC BY-SA