Groupoids of Local Isometries
The purpose of this chapter is to prove a general result concerning the developability of groupoids of local isometries. We shall show that if such a groupoid G is Hausdorff and complete (in a suitable sense, 2.10), and if the metric on the space of units of G is locally convex, then G is equivalent to the groupoid associated to the proper action of a group of isometries on a complete geodesic space whose metric is (globally) convex in the sense of (II.1.3). This result unifies and extends several earlier developability theorems, as we shall now explain.
KeywordsManifold Corson IlLy
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