Following the ideas of Exercises 7 and 8, prove that ∂² = 0 in general, i.e., that ∂_n-1 (∂_n(c)) = 0 for every c ∈ C_n(X), where n may be greater than 3.

Data from Exercise 7

Define the following concepts so as to generalize naturally the definitions in the text given for dimensions 0. 1, 2, and 3.