Łojasiewicz exponent of overdetermined semialgebraic mappings

We prove that both local and global Łojasiewicz exponent of a continuous overdetermined semialgebraic mapping F : X → Rᵐ on a closed semialgebraic set X ⊂ Rⁿ (i.e. m > dimX) are equal to the Łojasiewicz exponent of the composition L ₒ F : X → Rᵏ for the generic linear mapping L : Rᵐ → Rᵏ, where k = dimX

On C0-sufficiency of jets

The paper presents some details of the proofs by Kuiper and Kuo, and Bochnak and Łojasiewicz that refer to the impact of the Łojasiewicz exponent of gradient mappings on C0-sufficiency of jets