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Density of Morse functions on sets definable in o-minimal structures

100%

Loi T.

Annales Polonici Mathematici

2006

tom 89

nr 3

289-299

We present a tameness property of sets definable in o-minimal structures by showing that Morse functions on a definable closed set form a dense and open subset in the space of definable $C^p$ functions endowed with the Whitney topology.

Analytic cell decomposition of sets definable in the structure $ℝ_{exp}$

100%

Loi T.

Annales Polonici Mathematici

1994

tom 59

nr 3

255-266

We prove that every set definable in the structure $ℝ_{exp}$ can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.

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2 Annales Polonici Mathematici

2 Loi T.

1 2006

1 1994

Wyniki wyszukiwania

Density of Morse functions on sets definable in o-minimal structures

Analytic cell decomposition of sets definable in the structure $ℝ_{exp}$