I′ ∩ I″ = φ, such that dim(X′) = dim(X″), (9) where X′ = ⨂Xᵢ (10) I′ X″ = ⨂Xᵢ. I″ (If dim (X) is odd, then we have to cheat a little by putting in an extra random dummy dimension.) And then the decomposition of the space