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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Abstract Nash manifolds


Author: M. Shiota
Journal: Proc. Amer. Math. Soc. 96 (1986), 155-162
MSC: Primary 58A07
MathSciNet review: 813829
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0813829-5
PII: S 0002-9939(1986)0813829-5
Keywords: Nash manifold, real algebraic geometry, semialgebraic set
Article copyright: © Copyright 1986 American Mathematical Society