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Definable stratification satisfying the Whitney property with exponent 1

100%

Kocel-Cynk B.

Annales Polonici Mathematici

2007

tom 92

nr 2

155-162

We prove that for a finite collection of sets $A₁,...,A_s ⊂ ℝ^{k+n}$ definable in an o-minimal structure there exists a compatible definable stratification such that for any stratum the fibers of its projection onto $ℝ^k$ satisfy the Whitney property with exponent 1.

On the problem of Baer and Kolchin in the Picard-Vessiot theory

63%

Kocel-Cynk B., Sowa E.

Banach Center Publications

2011

tom 94

nr 1

215-220

We present the history of the development of Picard-Vessiot theory for linear ordinary differential equations. We are especially concerned with the condition of not adding new constants, pointed out by R. Baer. We comment on Kolchin's condition of algebraic closedness of the subfield of constants of the given differential field over which the equation is defined. Some new results concerning existence of a Picard-Vessiot extension for a homogeneous linear ordinary differential equation defined over a real differential field K with real closed field of constants F are also mentioned.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Banach Center Publications

2 Kocel-Cynk B.

1 Sowa E.

1 2011

1 2007

Wyniki wyszukiwania

Definable stratification satisfying the Whitney property with exponent 1

On the problem of Baer and Kolchin in the Picard-Vessiot theory