I need some help in answering this exercise from Serre's Local Fields textbook:
Let K be a complete field, and let f(X) in K[X] be a separable irreducible polynomial of degree n. Let L/K be the extension of degree n defined by f. Show that for every polynomial h(X) of degree n that is close enough to f, h(X) is irreducible and the extension (L_h)/K defined by h is isomorphic to L.