A folk theorem says that star-shaped open subsets of R^n are diffeomorphic to R^n.

Is there a citeable reference for 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.)

American Mathematical Monthly,Expositiones Mathematicae(Elsevier, though!),Confluentes Mathematicietc (sourced from mathoverflow.net/questions/15366/…). Also, some relevant discussion/references is in ncatlab.org/nlab/show/ball $\endgroup$ – David Roberts Mar 2 '15 at 22:39Convex Regions in the Geometry of Paths, Quart. J. Math.3(1932) 33-42). A proof valid for any manifold with an affine connection (not just Riemannian) may be found in the charming (although unfortunately out-of-print) little book of Noel J. Hicks (the same from the Cartan-Ambrose-Hicks theorem),Notes on Differential Geometry(Van Nostrand, 1965), Section 9.4, pp. 134-136. $\endgroup$ – Pedro Lauridsen Ribeiro Jun 11 '16 at 3:32