RT Journal Article
T1 Molino's description and foliated homogeneity
A1 Álvarez López, Jesús Antonio
A1 Barral Lijó, Ramón
K1 Foliated space
K1 Equicontinuous
K1 Strongly quasi-analytic
K1 Molino's description
K1 Foliated homogeneous
AB The 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.
PB Elsevier
SN 0166-8641
YR 2019
FD 2019-06-15
LK http://hdl.handle.net/10347/32076
UL http://hdl.handle.net/10347/32076
LA eng
NO Álvarez López, J.A., Barral Lijó, R. (2019). Molino's description and foliated homogeneity. "Topology App.", vol. 260, 148-177.
NO MICINN, grant MTM2014-56950-P; Xunta de Galicia, grant 2015 GPC GI-1574.
DS Minerva
RD 24 abr 2026