Abstract Nash Manifolds
Masahiro Shiota · Proceedings of the American Mathematical Society · 1986
We prove that any abstract noncompact Nash manifold is ${C^\infty }$ diffeomorphic to the interior of some compact ${C^\infty }$ manifold with boundary, and conversely, that such an interior or a compact ${C^\infty }$ manifold admits infinitely many abstract Nash manifold structures. The last result is a generalization of [2], where the case of a torus is proved.