Sub subsequences suppose that (m, d) is a metric space and a∈m. suppose further that (xk)k is a sequence in m with the property that every subsequence of (xk)k has a further subsequence which converges to a. show that (xk)k converges to a. give an example of a sequence (yk)k in some metric space, which does not converge but has the property that every subsequence has a further subsequence which does converge.