1. The problem statement, all variables and given/known data Let (X, d) be a metric space. The set Y in X , d(x; y) less than equal to r is called a closed set with radius r centred at point X. Show that a closed ball is a closed set. 2. Relevant equations In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points. 3. The attempt at a solution I have no idea, please help!