Abstract
We show for the class D of all C(infinity), transitive and topologically conjugate to algebraic polynomials interval self-maps the following stability type property: the class D has no isolated points and for every f is an element of D and any epsilon arbitrary small positive real number there exists a map g is an element of D sharing with f the same fixed points except one and such that parallel to f - g parallel to(1) = epsilon. On the contrary, we also show for each f is an element of D that there exists a C(infinity) interval self-map topologically conjugate to a polynomial, not transitive and parallel to.parallel to(1)-arbitrary close to the map f.