Is there a citeable reference for star-shaped open subsets of R^n being diffeomorphic to R^n? A folk theorem says that star-shaped open subsets of R^n are diffeomorphic to R^n.
Is there a citeable reference for a proof of this result?
For the sake of being definite, let's say that
“citeable” means indexed by Mathematical Reviews or Zentralblatt,
or available on arXiv.
The answer https://mathoverflow.net/a/4516 gives two references for this theorem, neither of which is citeable in the above sense: online notes and an obscure book, impossible to locate.  There are many citeable sources that state this result without a proof.
 A: The result in the following paper implies that open star-shaped domainin $\mathbb{R}^n$ is homeomorphic to $\mathbb{R}^n$.
But, in your case, a diffeomorphism can be obtained along the same lines.
K. W. Kwun. “Uniqueness of the open cone neighborhood”. Proc. Amer. Math. Soc.
15 (1964), pp. 476–479.
Postscript. Instead of a reference one could write the following lines:
Any star-shaped open set $\Omega$ is a union of a nested sequence of star-shaped open regions $\Omega_0\subset \Omega_1\subset\dots$ such that $\partial\Omega_n$ is a graph of a smooth Lipschitz function in the polar coordinates. We can assume that $\Omega_0$ is a disc; in particular $\Omega_0$ is diffeomorphic to $\mathbb{R}^n$.
Observe that for each $n$ there is a diffeomorphism $\phi_n\colon\bar \Omega_{n-1}\to\bar\Omega_n$; moreover we can assume that $\phi_n$ fix all points away from a tiny neightborhood of $\partial\Omega_n$. In particular, it can be arranged that for any $x_0\in \Omega_0$, the sequence defined by $x_n=\phi_n(x_{n-1})$ stabilizes after finitely many steps. Define $f(x_0)=x_n$ for all large $n$, and observe that $f\colon \Omega_0\to\Omega$ is a diffeomorphism.
A: This result is stated as Exercise 7 in Chapter 8 of Bröcker and Jänich's book Introduction to Differential Topology (p. 86 of the English translation). This may or may not count as a citeable reference.
