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Many Structures on a topological m- manifold M may be defined by means of an atlas of local coordinate systems for which the coordinate systems belong to some pseudo group P of transformations in the model space R.
To any symmetric affine connection ?on M there is associated a family of normal coordinate systems in a canonical way, via the exponential map. However, the coordinate transformations that occur within this family do not form a pseudo group of transformations in On the other hand, normal coordinate systems are »abundant« in the sense that there is at least one such system based at every point of M.
The purpose of this paper is to modify the pseudo group notion of structure to obtain a characterization of symmetric affine connections.