EDB — 0YD

Exercises

1. [0YD] Prerequisites:[0R2]↺↻.One can easily show that a function \(f:ℝ/2𝜋→ X\) can be seen as a periodic function \(\tilde f:ℝ→ X\) of period \(2𝜋\), and vice versa.

   This can be easily obtained from the relation \(f([t])=\tilde f(t)\) where \(t\) is a generic element of its equivalence class \([t]\). Assuming that \(\tilde f\) is periodic (with period \(2𝜋\)), the above relation allows to derive \(f\) from \(\tilde f\) and vice versa.

   Show that \(f\) is continuous if and only if \(\tilde f\) is continuous.