We prove the topological (or combinatorial) rigidity property for real polynomials with all critical points real and nondegenerate, which completes the last step in solving the density of Axiom A conjecture in real one-dimensional dynamics. Contents 1. Introduction . Statement of results . Organization of this work . General terminologies and notation 2. Density of Axiom A follows from the Rigidity Theorem 3. Derivation of the Rigidity Theorem from the Reduced Rigidity Theorem