P. Foulon, FOLIATIONS OF SPHERES AND NORTH-SOUTH DYN AMICS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 318(11), 1994, pp. 1041-1042
One shows that on a closed manifold there is no non trivial C0-foliati
on with only two foliating charts. One then deduces that a C0 invarian
t by a North-South dynamic is trivial i.e. either its dimension or its
codimension is zero.