Functions on the zeroes of dxdx

In the model FF of synthetic differential geometry consisting of sheaves (with respect to open covers) over FF, the opposite category of the category of closed finitely generated C∞C∞-rings, any morphism from S  , the zeroes of the “amazing right adjoint” of dxdx, 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 dxdx.