2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228090The 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.12 pages, LaTeX. v1 to v2: Results unchanged. Presentation improved: Sect. 4 restructured (proof of Cor. 4.5 as well); some comments added; reference updatedMathematical PhysicsGeneral Relativity and Quantum Cosmology34C27 (Primary) 53C05, 83F05 (Secondary)text