Zorich's theorem

In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967.^[1] The result was conjectured by M. A. Lavrentev in 1938.^[2]

Theorem

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

The fact that there is no such result for ${\displaystyle n=2}$ is easily shown using the exponential function.^[4]