mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

, 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 In mathematics and more specifically in topology, a homeomorphism ( from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function betw ...

quasiregular map In the mathematical field of analysis, quasiregular maps are a class of continuous maps between Euclidean spaces R''n'' of the same dimension or, more generally, between Riemannian manifolds of the same dimension, which share some of the basic prop ...

ping

f : R^ \rightarrow R^

for

n \geq 3

, is a homeomorphism of

R^

. The fact that there is no such result for

n = 2

is easily shown using the exponential function.

References

General topology Theorems in topology Conjectures that have been proved {{mathanalysis-stub