论文标题
秋季拓扑结构和模块化的Gromov-Hausdorff Propinquity
The Fell topology and the modular Gromov-Hausdorff propinquity
论文作者
论文摘要
考虑到配备了忠实的奇特状态的Unital Af-Algebra $ a $，我们为$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a的量子矢量束结构装备时，当在latrémolière上以$ a $ $ a的模块视为模块时，使用了先前的第一作者和litrémolière和litrémolière和litrémolière。此外，我们表明，秋季拓扑中理想的融合意味着在latrémolière模块化的Gromov-Hausdorff prominquity中相关的Metrized量子矢量束的融合。在类似的方面，但需要采用不同的方法，鉴于紧凑的度量空间$（x，d）$，我们为$ c（x）$的每个理想配备了Metrrized量子矢量束结构，并表明秋季拓扑中的融合意味着在模块化的Gromov-Hausdorff propinquity中收敛。
Given a unital AF-algebra $A$ equipped with a faithful tracial state, we equip each (norm-closed two-sided) ideal of $A$ with a metrized quantum vector bundle structure, when canonically viewed as a module over $A$, in the sense of Latrémolière using previous work of the first author and Latrémolière. Moreover, we show that convergence of ideals in the Fell topology implies convergence of the associated metrized quantum vector bundles in the modular Gromov-Hausdorff propinquity of Latrémolière. In a similar vein but requiring a different approach, given a compact metric space $(X,d)$, we equip each ideal of $C(X)$ with a metrized quantum vector bundle structure, and show that convergence in the Fell topology implies convergence in the modular Gromov-Hausdorff propinquity.
