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The holonomy groupoid of a locally topological groupoid. (English) Zbl 0855.22007

Summary: We deal with the globalization of a topology on a subset \(W\) of a groupoid \(G\), such that \(W\) contains the identities of \(G\). The classical situation for groups, namely extendability of the topology under suitable conditions, fails in general for groupoids, but the topology does, under suitable conditions, globalize to a topology on the holonomy groupoid \(\text{Hol} (G, W)\), which maps onto \(G\). The construction is due to J. Pradines (unpublished). Full details and proofs of the results, with some improvements, are given.

MSC:

22A22 Topological groupoids (including differentiable and Lie groupoids)
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
18F05 Local categories and functors
57R30 Foliations in differential topology; geometric theory
58H05 Pseudogroups and differentiable groupoids
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