Lemma 3.8 . [00KG]

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Lemma 3.8.

Let $\lVert\mathord{\cdot}\rVert_{n}$ be a norm on $V_{n}(L)$ , then $\frac{1}{n}\mathrm{FS}(\lVert\mathord{\cdot}\rVert_{n})$ is a continuous metric on $L$ . ([CMor18, Proposition 3.1])