1. The problem statement, all variables and given/known data X is a compact metric space, X/≈ is the quotient space,where the equivalence classes are the connected components of X.Prove that X/ ≈ is metrizable and zero dimensional. 2. Relevant equations Y is zero dimensional if it has a basis consisting of clopen (closed and open at the same time) 3. The attempt at a solution I thought that Uryson's metrization theorem may be used.I considered also the metric given in wikipedia.