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Graph Groupoids and Their Topology:

ISBN-10: 3639007484
ISBN-13: 9783639007480
Edition: 2008
Authors: Adrian Wilson
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Description: The book investigates graph groupoids and the path spaces associated with their unit spaces. Three main questions are solved. For the first, a natural question that was asked by A.Kumjian in the case of the Cuntz graph was how the topological space  More...

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Book details

Copyright year: 2008
Publisher: Vdm Verlag Dr Mueller E K
Binding: Paperback
Pages: 84
Language: English

The book investigates graph groupoids and the path spaces associated with their unit spaces. Three main questions are solved. For the first, a natural question that was asked by A.Kumjian in the case of the Cuntz graph was how the topological space X relates to an earlier topological space investigated by J. Renault (Orleans). I show that the two topological spaces are homeomorphic and so can be identified. I then discuss the graph groupoid in the general case. For this investigation, it is important to be able to use the axiomatic approach to groupoids, and I show that this is equivalent to the usual definition of a groupoid as a "small category with inverses." This proof of this equivalence answers the second main question. The last is to construct the graph groupoid and prove that it is a second countable, locally compact, Hausdorff groupoid.

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