Let f: (R, de) → (R2, de) be defined by f(x) = (x,x) for all x ER. (a) Is f an isometry? Give a brief justification of your answer. (b) Is f continuous? Give a brief justification of your answer. (c) Let A = {(x,x): x = R} and g: (R, dE) → (A, de) be defined by g(x) = (x,x) for all x ER. Prove that g is a topological isomorphism, that is, a homeomorphism. Be sure to mention explicitly all the properties that need to be checked.