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 → R n {\displaystyle f:R^{n}\rightarrow R^{n}} for n ≥ 3 {\displaystyle n\geq 3} , is a homeomorphism of R n {\displaystyle R^{n}} . The fact that there is no such result for n = 2 {\displaystyle n=2} is easily shown using the exponential function.
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