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 $f:R^n\to R^n$ for $n\ge 3$, is a homeomorphism of $R^n$.

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

References

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