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 (m ...

, Zorich's theorem was proved by

Vladimir A. Zorich Vladimir Antonovich Zorich (''Владимир Антонович Зорич''; born 16 December 1937, Moscow) is a Soviet and Russian mathematician, Doctor of Physical and Mathematical Sciences (1969), Professor (1971). Honorary Professor of Mos ...

in 1967. The result was conjectured by M. A. Lavrentev in 1938.

Theorem

Every locally

homeomorphic In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphi ...

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 pro ...

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 The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, a ...

References

General topology {{mathanalysis-stub