What sort of example would make the following this false if 'D is compact' is replaced by 'D is closed'?

Let (Y,d) be a metric space and let C, D be non-empty subsets of Y such that: C is closed, D is compact, and C ∩ D = ∅. Show that d(c,d) >= 0 for c ϵ C, d ϵ D.