有向图的道路空间
The Path Space of a Directed Graph
摘要：
在有向图$E$的道路空间上构造了一个局部紧Hausdorff拓扑，并将其边界道路空间$\partial E$确定为$C^*(E)$的交换$C^*$ -子代数$D_E$的谱.然后，我们表明，$\partial E$同胚的一个子集的无限道路空间的任何desingularisation $F$的$E$。Drinen和Tomforde证明了可以将$C^*(E)$实现为$C^*(F)$的一个全角，并推导出$D_E$同构于$D_F$的一个角.最后，我们证明了这种同构实现了边界-路空间之间的同胚.
英文摘要：
We construct a locally compact Hausdorff topology on the path space of a directed graph $E$, and identify its boundary-path space $\partial E$ as the spectrum of a commutative $C^*$-subalgebra $D_E$ of $C^*(E)$. We then show that $\partial E$ is homeomorphic to a subset of the infinite-path space of any desingularisation $F$ of $E$. Drinen and Tomforde showed that we can realise $C^*(E)$ as a full corner of $C^*(F)$, and we deduce that $D_E$ is isomorphic to a corner of $D_F$. Lastly, we show that this isomorphism implements the homeomorphism between the boundary-path spaces.
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