A set on which the local Łojasiewicz exponent is attained

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Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping

F = (f ₁, ..., f ₘ) : U \to ℂ^{m}

, F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set {z ∈ U: f₁(z)·...·fₘ(z) = 0}.

holomorphic mapping, Łojasiewicz exponent

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