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The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class (D_n(Σ^0_2)) for some natural number n≥ 1, where is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space 2^ω into the class Δ^1_2, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual Δ^1_2.arXiv:1503.02840v2 fatcat:fpifejyktvbqvixcedk6ishtqe