Es sei \( v_{\underline{k}}=\left(x_{\underline{k}}, y_{\underline{k}}\right) \in\left(\mathbb{R}^{2}\right)^{\mathbf{N}} . \) Dann gilt fur \( v_{\infty}=\left(x_{\infty}, y_{\infty}\right) \in \mathbb{R}^{2} \)
$$ v_{k} \underset{k \rightarrow \infty}{\longrightarrow} v_{\infty} \Longleftrightarrow x_{k} \underset{k \rightarrow \infty}{\longrightarrow} x_{\infty} \wedge y_{k} \underset{k \rightarrow \infty}{\longrightarrow} y_{\infty} . $$
a) In der Manhatten-Norm.
b) In der Maximum-Norm.
