Displaying similar documents to “Computing the dimension of a semi-algebraic set.”

On the polynomial-like behaviour of certain algebraic functions

Charles Feffermann, Raghavan Narasimhan (1994)

Annales de l'institut Fourier

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Given integers D > 0 , n > 1 , 0 < r < n and a constant C > 0 , consider the space of r -tuples P → = ( P 1 ... P r ) of real polynomials in n variables of degree ≤ D , whose coefficients are ≤ C in absolute value, and satisfying det ∂ P i ∂ x i ( 0 ) 1 ≤ i , j ≤ r = 1 . We study the family { f | V } of algebraic functions, where f is a polynomial, and V = { | x | ≤ δ , P → ( x ) = 0 } , δ > 0 being a constant depending only on n , D , C . The main result is a quantitative extension theorem for these functions which is uniform in P → . This is used to prove Bernstein-type inequalities which are again uniform with respect to P → . ...

On some global semianalytic sets

Abdelhafed Elkhadiri (2013)

Annales de l’institut Fourier

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We give some structures without quantifier elimination but in which the closure, and hence the interior and the boundary, of a quantifier free definable set is also a quantifier free definable set.