  The set of homogeneous isotropic connections, as used in loop quantum
cosmology, forms a line $l$ in the space of all connections $\cal A$. This
embedding, however, does not continuously extend to an embedding of the
configuration space $\overline l$ of homogeneous isotropic loop quantum
cosmology into that of loop quantum gravity, $\overline{\cal A}$. This follows
from the fact that the parallel transports for general, non-straight paths in
the base manifold do not depend almost periodically on $l$. Analogous results
are given for the anisotropic case.
