Álvarez López, Jesús AntonioBarral Lijó, Ramón2024-01-302024-01-302019-06-15Álvarez López, J.A., Barral Lijó, R. (2019). Molino's description and foliated homogeneity. "Topology App.", vol. 260, 148-177.0166-8641http://hdl.handle.net/10347/32076The topological Molino's description of equicontinuous foliated spaces, studied by the first author and Moreira Galicia, gives conditions to reduce their study to the particular case of $G$-foliated spaces. That description is sharpened in this paper by introducing a foliated action of a compact topological group on the resulting $G$-foliated space, like in the case of Riemannian foliations. Moreover a $C^\infty$ version is also studied. The triviality of this compact group characterizes compact minimal $G$-foliated spaces, which are also characterized by their foliated homogeneity in the $C^\infty$ case. We also give an example where the projection of the Molino's description is not a principal bundle, and another example of positive topological codimension where the foliated homogeneity cannot be checked by only comparing pairs of leaves---in the case of zero topological codimension, weak solenoids with this property were given by Fokkink and Oversteegen, and later by Dyer, Hurder and Lukina.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Foliated spaceEquicontinuousStrongly quasi-analyticMolino's descriptionFoliated homogeneous110206 Fundamentos de matemáticasjournal article10.1016/j.topol.2019.04.0041879-3207open access