Alexander–Spanier cohomology

Summary

Alexander–Spanier cohomology is a cohomology theory for topological spaces built from arbitrary functions on tuples of points, taken modulo functions that vanish near the diagonal. It does not use simplices or maps from a model space, so it behaves well on spaces with bad local structure. On paracompact Hausdorff spaces it agrees with Čech cohomology and with sheaf cohomology of a constant sheaf. On manifolds and CW complexes it agrees with singular cohomology.