A simple proof of Zahorski's description of non-differentiability sets of Lipschitz functions (Q1029983)

A simple proof of the following theorem of Zahorski it is given: Given any \(G_{\delta\sigma}\) set \(G\subset{\mathbb R}\) of measure zero, there exists a Lipschitz function \(g:{\mathbb R}\rightarrow{\mathbb R}\) which is differentiable everywhere on \({\mathbb R}\setminus G\) and non-differentiable everywhere on \(G\). The proof does not rely on a geometric construction as Zahorski's original proof, but on a simple topological argument.