EDB — 1PG

[1PG] Let \(𝛾:[0,1]\to {\mathbb {R}}^ n\) be a closed \(C^ 1\) curve, show that it admits an extension \(\tilde𝛾:{\mathbb {R}}\to {\mathbb {R}}^ n\) periodic with period \(1\) and of class \(C^ 1\).