title: Zorich's theorem
text: # 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.
  
  