Canonical forms of Borel-measurable mappings Δ: [ω] →

We show that for every Borel-measurable mapping Δ: ω]^ω → there exists A ω]^ω and there exists a continuous mapping Γ: A]^ω → A]^ω with Γ(X) X such that for all X, Y A]^ω it follows that Δ(X) = Δ(Y) if Γ(X) = Γ(Y). In a sense, this is generalization of the Erdös-Rado canonization theorem