Zorich's theorem
# 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.

## Theorem

Every locally homeomorphic quasiregular mapping ƒ : $R^n$ → $R^n$ for n ≥ 3, is a homeomorphism of $R^n.$

The fact that there is no such result for n = 2 is easily shown using the exponential function.

