EDB — 1PN

[1PN]Prerequisites:[1NW]↺↻,[1PF]↺↻.Let \(𝛾,𝛿\) be closed curves, but seen as maps defined on \(ℝ\), continuous and periodic of period \(1\).

Let’s discuss a new relation: we write \(𝛾∼_ f𝛿\) if there is an increasing homeomorphism \(𝜑:ℝ→ℝ\) such that \(𝜑(t+1)=𝜑(t)+1\) for every \(t∈ℝ\), and for which \(𝛾=𝛿 ◦𝜑\)

Show that this is an equivalence relation.

Compare it with the relation \(∼\).