2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184950When the topology of the universe is non trivial, it has been shown that there are constraints on the network of domain walls, cosmic strings and monopoles. I generalize these results to textures and study the cosmological implications of such constraints. I conclude that a large class of multi-connected universes with topological defects accounting for structure formation are ruled out by observation of the cosmic microwave background.4 pages, 1 figure, accepted for publication as a brief report in Phys. Rev. DGeneral Relativity and Quantum Cosmologytext