Álvarez López, Jesús AntonioBarral Lijó, RamónCandel, Alberto2024-02-092024-02-092016Álvarez López, J.A., Barral Lijó, R., Candel, A. (2016). A universal Riemannian foliated space. "Topology and its Applications", vol. 198, 47-85.0166-8641http://hdl.handle.net/10347/32662It is proved that the isometry classes of pointed connected complete Riemannian n-manifolds form a Polish space X with the topology described by the smooth convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifold. The locally non-periodic manifolds define an open dense subspace Y, which becomes a smooth foliated space with the restriction of the canonical partition. Its leaves without holonomy form the subspace Z defined by the non-periodic manifolds. Moreover, the leaves have a natural Riemannian structure so that Y becomes a Riemannian foliated space, which is universal among all sequential Riemannian foliated spaces satisfying certain property called covering-determination. Y is used to characterize the realization of complete connected Riemannian manifolds as dense leaves of covering-determined compact sequential Riemannian foliated spaces.engCC BY-NC-ND 4.0http://creativecommons.org/licenses/by-nc-nd/4.0/Locally non-periodic Riemannian manifoldsRiemannian foliated spaceSmooth convergence of Riemannian manifolds12 Matemáticasjournal article10.1016/j.topol.2015.11.0061879-3207open access