Let $V$ and $W$ be normed spaces over the same scalar field $\mathbb{F}$, where $\mathbb{F}\in\{\mathbb{R},\mathbb{C}\}$. Equip $V\times W$ with the usual product [vector space](/page/Vector%20Space) structure. Define maps
Then $\|\cdot\|_1$ and $\|\cdot\|_\infty$ are norms on $V\times W$, and the norm topology induced by each of these norms is equal to the [product topology](/page/Product%20Topology) of the norm topologies on $V$ and $W$.