De Rham showed that all of these approaches were interrelated and that, for a closed, oriented manifold, the Betti numbers derived through simplicial homology were the same Betti numbers as those derived through de Rham cohomology.
De Rham demostrou que todos estes tipos de aproximación están interrelacionados e que os números de Betti que se derivan da homoloxía simplicial eran os mesmos números de Betti que aqueles que se derivan da cohomoloxía de De Rham.