Thus let xm→p,{xm}⊆A. As A is compact, the sequence {xm} clusters at some q∈A, i.e., has a subsequence \(x_{m_{k}} \righta...Thus let xm→p,{xm}⊆A. As A is compact, the sequence {xm} clusters at some q∈A, i.e., has a subsequence xmk→q∈A. However, the limit of the subsequence must be the same as that of the entire sequence.
