Alexander-Spanier Cohomology

A fundamental result of de Rham Cohomology is that the $k$th de Rham Cohomology Vector Space of a Manifold $M$ is canonically isomorphic to the Alexander-Spanier cohomology Vector Space $H^k(M;\Bbb{R})$ (also called cohomology with compact support). In the case that $M$ is Compact, Alexander-Spanier cohomology is exactly ``singular'' Cohomology.