Let $(X,d)$ be a [metric space](/page/Metric%20Space), let $Y\subset X$, and let $d_Y:Y\times Y\to [0,\infty)$ be the subspace metric defined by $d_Y(a,b)=d(a,b)$ for all $a,b\in Y$. If $(y_k)_{k=1}^{\infty}$ is a sequence in $Y$ and $y\in Y$, then $(y_k)_{k=1}^{\infty}$ converges to $y$ in the metric space $(Y,d_Y)$ if and only if $(y_k)_{k=1}^{\infty}$ converges to $y$ in the metric space $(X,d)$.