## Separated nets in Euclidean space and Jacobians of biLipschitz maps.(English)Zbl 0902.26004

A subset $$X$$ of a metric space $$Z$$ is a separated net if there are constants $$a,b> 0$$ such that $$d(x,x')> a$$ for every pair $$x,x'\in X$$ and $$d(z,X)< b$$ for every $$z\in Z$$.
The authors show the existence of separated nets in the Euclidean plane which are not bi-Lipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a bi-Lipschitz map.

### MSC:

 26B10 Implicit function theorems, Jacobians, transformations with several variables
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