A subset A of a metric space X is called uniformly discrete if there

epsilon> 0 with the property that the distance between two distinct points of A is always

greater or equal to epsilon:

∀ a, b ∈ A, (a!= b) ⇒ (dX (a, b) ≥ epsilon).

Show that any subset of a uniformly discrete metric space X is

closed in X.