The Path Space of a Directed Graph
نویسنده
چکیده
We construct a locally compact Hausdorff topology on the path space of a directed graph E and identify its boundary-path space ∂E as the spectrum of a commutative C∗-subalgebra DE of C∗(E). We then show that ∂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 DE is isomorphic to a corner of DF . Lastly, we show that this isomorphism implements the homeomorphism between the boundary-path spaces.
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