A way to ensure the existence of limits of certain infinite series is to restrict attention to spaces where any Cauchy sequence has a limit; such a vector space is called complete. Roughly, a vector space is complete provided that it contains all necessary limits. For example, the vector space of polynomials on the unit interval equipped with the topology of uniform convergence is not complete because any continuous function on [0,1 can be uniformly approximated by a sequence of polynomials, by the Weierstrass approximation theorem. In contrast, the space of "all" continuous functions on [0,1] with the same topology is complete. A norm gives rise to a topology by defining that a sequence of vectors v"n" converges to v if and only if