Let ( M , d ) {\displaystyle {}(M,d)} be a metric space, and let ( x n ) n ∈ N {\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} }} denote a sequence in M {\displaystyle {}M} . Show that the sequence converges in the sense of a metric space if and only if the sequence converges in the sense of topology.
