将空间的罗伊代数与空间离散化的统一罗伊代数联系起来

Abstract The Roe algebra \(C^{*}(X)\) is a non-commutative \(C^{*}\)-algebra reflecting metric properties of a space \(X\), and it is interesting to understand relation between the Roe algebra of \(X\) and the uniform Roe algebra of its discretizations.在这里，我们为简单空间 \(X\)构造了一个在 \(\mathbb{N}\cup\{infty\)上的\(C^{*}\)-代数的连续域，其在有限点上的纤维是 \(X\)离散化的统一\(C^{*}\)-代数，而在\(\infty\)上的纤维是 \(X\)的罗伊代数。）我们还构造了离散化的统一 Roe 代数的直接极限以及它对\(X\)的 Roe 代数的嵌入。