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It is known that every germ of an analytic set is homeomorphic to the germ ofan algebraic set. In this paper we show that the homeomorphism can be chosen insuch a way that the analytic and algebraic germs are tangent with anyprescribed order of tangency. Moreover, the space of arcs contained in thealgebraic germ approximates the space of arcs contained in the analytic one, inthe sense that they are identical up to a prescribed truncation order.

Higher order approximation of analytic sets by topologically equivalent algebraic sets