Structure spaces of approximately finite-dimensional C∗-algebras, II
Structure spaces of approximately finite-dimensional C∗-algebras, II
复制标题
近似有限维 C*-代数的结构空间，II
DOI：
10.1016/0022-1236(78)90056-3
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发表时间：
1974
影响因子：
1.7
通讯作者：
O. Bratteli
中科院分区：
文献类型：
--
作者：
O. Bratteli
考虑拓扑空间的以下性质：(1)不同的点具有不同的闭包（t0分离）。(2)每个不是两个固有闭子集并集的闭集是一个点的闭集。(3)存在可数基础。(4)存在紧开集的一个基。已知可分离的近似有限维c * -代数的原始理想空间具有(1)-(4)的性质。我们将证明任何具有性质(1)-(4)的空间都以这种方式产生。
Consider the following properties of a topological space: (1) Distinct points have distinct closures (T0separation). (2) Each closed set not the union of two proper closed subsets is the closure of a point. (3) There exists a countable basis. (4) There exists a basis of compact open sets. It is known that the space of primitive ideals of a separable approximately finite-dimensionalC∗-algebra has properties (1)–(4). We shall show that any space with properties (1)–(4) arises in this way.