 There are also homology groups formula_254 of a space, and indeed these were defined first, as a useful tool for distinguishing between certain pairs of topological spaces, like the spheres and tori, for which the methods of point-set topology are not well-suited.Cohomology groups were later defined in terms of homology groups in a way which is roughly analogous to the dual of a vector space.To know each individual integral homology group is essentially the same as knowing each individual integral cohomology group, because of the universal coefficient theorem.