Functions on the zeroes of dx

In the model image of synthetic differential geometry consisting of sheaves (with respect to open covers) over image, the opposite category of the category of closed finitely generated C∞-rings, any morphism from S, the zeroes of the “amazing right adjoint” of dx, to the real line R extends to a morphism from R to R. This shows that the De Rham cohomology of the space S is the same as the characteristic cohomology of the ideal generated by dx.