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AFFINENESS OF DEFINABLE Cr MANIFOLDS AND ITS APPLICATIONS
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 Title & Authors
AFFINENESS OF DEFINABLE Cr MANIFOLDS AND ITS APPLICATIONS
Kawakami, Tomohiro;
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 Abstract
Let M be an exponentially bounded o-minimal expansion of the standard structure R = (R ,+,.,<) of the field of real numbers. We prove that if r is a non-negative integer, then every definable manifold is affine. Let f : X Y be a definable map between definable manifolds. We show that the set S of critical points of f and f(S) are definable and dim f(S) < dim Y. Moreover we prove that if 1 < s < < , then every definable manifold admits a unique definable manifold structure up to definable diffeomorphism. 炭᠂ ࠀ豈檧Ā檧Ā̀￿￿֗⨀Ā�ĀĀၧ잖⨀̀ĀĀ逅—⨀倅—⨀؀肀ქヨ⨀밟Ԁꀮ֗⨀⃬│胫│惭│郭│塻җ⨀뀯֗⨀찟퀟퀄—⨀Ԁ怯֗⨀í│탫│惭│烮│찟퀟퀄—⨀퀟ഀĀ顪—⨀Ā偫—⨀㠈—⨀ဩ—⨀Ȁᠩ—⨀—⨀⬀Ā 堪—⨀젪—⨀阁Ā1֗⨀⡧잖⨀̀⡧잖⨀̀܀屣잖⨀ࠀ褝⎨Ā⎨Ā̀￿￿屣잖⨀檧Ā䁧잖⨀聧잖⨀֗⨀�җ⨀堵֗⨀ഀ Ā
 Keywords
definable manifolds;definable maps;o-minimal;Sard's theorem;expotentionally bounded;
 Language
English
 Cited by
 References
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