Consequently, if v \in \R^{\infty} and v_{\bull} is a sequence in \R^{\infty} then v_{\bull} \to v in \left(\R^{\infty}, \tau^{\infty}\right) if and only if there exists some n \in \N such that both v and v_{\bull} are contained in \operatorname{Im} \left( \operatorname{In}_{\R^n} \right) and v_{\bull} \to v in \operatorname{Im} \left( \operatorname{In}_{\R^n} \right).
