(Tricky) Suppose {Un}n=1∞ is a decreasing (Un+1⊂Un for all n) sequence of open sets in a metric space (X,d) such that ⋂n=1∞Un={p} for some p∈X. Suppose {xn}n=1∞ is a sequence of points in X such that xn∈Un. Does {xn}n=1∞ necessarily converge to p? Prove or construct a counterexample.