I have a problem that I need help to prove, can anyone please suggest any proof?
Suppose we have, closed parametric curve $f(t)=(x(t),y(t))'$ for $t\in (0,2\pi)$ (here, map is $f:(0,2\pi)\rightarrow\mathbb R^2$). How to prove that collection(space) of all such curves is a manifold?