Differentiable maps having hyperbolic sets

We show that the set of all Cr-differentiable maps satisfying both Axiom A and the strong transversality is open with respect to the Cr-topology (r ⩾ 1). This was proved by Newhouse and Palis for the class of Cr-diffeomorphisms. However, it also is obtained from the structural stability theorem for Cr-diffeomorphisms by Robbin and Robinson.