A set on which the local Łojasiewicz exponent is attained Jacek Chądzyński, Tadeusz Krasiński (1997) Annales Polonici Mathematici Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping F = ( f ₁ , . . . , f ₘ ) : U → ℂ m , F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set z ∈ U: f₁(z)·...·fₘ(z) = 0.