Given a uniform space (S, U ), a net {xα }α∈I in S is called a Cauchy net iff for any V ∈ U there is a γ ∈ I such that (xα, xβ )∈ V whenever α ≥ γ and β ≥ γ. The uniform space is called complete if every Cauchy net converges to some element of S (for the topology of U ). If a metric space (S, d) is complete, prove it is also complete as a uniform space.