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VOL. 43 | 2006 $(r)$ does not imply $(n)$ or $(npf)$ for definable sets in non polynomially bounded o-minimal structures
David Trotman, Leslie Wilson

Editor(s) Shyuichi Izumiya, Goo Ishikawa, Hiroo Tokunaga, Ichiro Shimada, Takasi Sano


It is known that if two subanalytic strata satisfy Kuo's ratio test, then the normal cone of the larger stratum $Y$ along the smaller $X$ satisfies two nice properties: the fiber of the normal cone at any point of $X$ is the tangent cone to the fiber of $Y$ over that point; the projection of the normal cone to $X$ is open ("normal pseudo-flatness"). We present an example with $X$ a line and $Y$ a surface which is definable in any non polynomially bounded o-minimal structure such that the pair satisfies Kuo's ratio test, but neither of the above properties hold for the normal cone.


Published: 1 January 2006
First available in Project Euclid: 3 January 2019

zbMATH: 1132.58004
MathSciNet: MR2325151

Digital Object Identifier: 10.2969/aspm/04310463

Rights: Copyright © 2006 Mathematical Society of Japan


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