Differentiability at a point a implies continuity in a neighborhood of a

Question

Let f be a map from a open subset U of a normed vector space E to an other F, suppose that f is differentiable at a point a in U. Is f continuous in a neighborhood of a ?

Answer 1

False: $$f(x) = \cases{ x^2& for $x\in\Bbb Q$,\cr 0& for $x\not\in\Bbb Q$.}$$