Abstract Nash manifolds

Shiota, M.

doi:10.1090/S0002-9939-1986-0813829-5

Abstract Nash manifolds
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by M. Shiota

Proc. Amer. Math. Soc. 96 (1986), 155-162

DOI: https://doi.org/10.1090/S0002-9939-1986-0813829-5

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Abstract:

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.

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Equivariant real algebraic differential topology

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