Lemma 3.5 . [03DY]

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Lemma 3.5.

Let $K$ be a subcomplex of $\operatorname{bsd}(T)$ , and let $N$ be a neighborhood of $K$ . Then there is a $\delta$ -realization of $\operatorname{bsd}(T,T)$ such that for each face $\mathfrak{T}$ of $K$ , the faces of $\operatorname{bsd}(T,T)$ which correspond to some $(\tau,$ $\mathfrak{T}$ $)$ are contained in $N$ .