If X is a topological space and G is an abelian group, then there is a complex C whose pth term Cp is the set of all functions from Xp+1 to G with differential d given by
It has a subcomplex C0 of functions that vanish in a neighborhood of the diagonal. The Alexander–Spanier cohomology groups Hp(X,G) are defined to be the cohomology groups of the complex C/C0.
Connection to other cohomologies
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