中文摘要：

我们为公制的空格的 subspaces 在这笔记介绍合适的公制的空格和 asymptotic 等价关系的 asymptotic 切除的观点，它在描绘 asymptotic 的空间理想是相关的粗糙的牝鹿代数学。我们证明一个合适的公制的空格的 subspaces 的 asymptotic 等价班的格子对 asymptotic 牝鹿代数学的空间理想的格子同形。为公制的空间的 asymptotic 切除，我们也在 asymptotic 的 K 理论建立一个 Mayer-Vietoris 序列粗糙的牝鹿代数学。

英文摘要：

We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a MayeroVietoris sequence in K-theory of the asymptotic coarse Roe algebras.