Topological Molino's theory

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Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to such a foliated space. As an application, we obtain a partial generalization of results by Carrière and Breuillard-Gelander, relating the structural local group to the growth of the leaves.