Lemma 5.5 . [00M2]

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Lemma 5.5.

Assume that $\phi$ is a Fubini-Study metric. For any $\epsilon>0$ , there exists $\boldsymbol{\delta}\in\mathbb{R}^{d+1}$ with $|\boldsymbol{\delta}|\leq\epsilon$ such that

\forall n\in\mathbb{N},\quad\dist(\lVert\mathord{\cdot}\rVert_{n\phi},\lVert\mathord{\cdot}\rVert_{n\phi(\boldsymbol{\delta})})\leq n\epsilon.