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 $$f : R^{n} \rightarrow R^{n}$$ for $$n \geq 3$$, is a homeomorphism of $$R^{n}$$.

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