Zorich's theorem

In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967. The result was conjectured by M. A. Lavrentev in 1938.

Every locally homeomorphic quasiregular mapping ${\displaystyle f:R^{n}\rightarrow R^{n}}$for ${\displaystyle n\geq 3}$, is a homeomorphism of ${\displaystyle R^{n}}$.

The fact that there is no such result for ${\displaystyle n=2}$is easily shown using the exponential function.