EVERY DEFINABLE Cr MANIFOLD IS AFFINE

Title & Authors
EVERY DEFINABLE Cr MANIFOLD IS AFFINE
KAWAKAMI, TOMOHIRO;

Abstract
Let M = (R, +, $\small{\cdot}$, <, ... ) be an o-minimal expansion of the standard structure R = (R, +, $\small{\cdot}$, >) of the field of real numbers. We prove that if 2 $\small{\le}$ r < $\small{\infty}$, then every n-dimensional definable $\small{C^r}$ manifold is definably $\small{C^r}$ imbeddable into $\small{R^{2n+l}}$. Moreover we prove that if 1 < s < r < $\small{\infty}$, then every definable $\small{C^s}$ manifold admits a unique definable $\small{C^r}$ manifold structure up to definable $\small{C^r}$ diffeomorphism.ﶖ⨀ᔌ넀؀㔷〮㔻Ԁ䭃䑎䷗ᜓ੹5㘰㬅K䍄乍숗ጊ㤀Ѐ㔷㔻Ԁ䭃䑎䴀
Keywords
definable C$\small{^r}$ manifolds;o-minimal;affine;
Language
English
Cited by
1.
DEFINABLE Cr FIBER BUNDLES AND DEFINABLE CrG VECTOR BUNDLES,;

대한수학회논문집, 2008. vol.23. 2, pp.257-268
1.
Smooth functions in o-minimal structures, Advances in Mathematics, 2008, 218, 2, 496
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