Just as in the case of an ordinary manifold, the supermanifold is then defined as a collection of charts glued together with differentiable transition functions. This definition in terms of charts requires that the transition functions have a smooth structure and a non-vanishing Jacobian. This can only be accomplished if the individual charts use a topology that is considerably coarser than the vector-space topology on the Grassmann algebra. This topology is obtained by projecting formula_13 down to formula_5 and then using the natural topology on that. The resulting topology is "not" Hausdorff, but may be termed "projectively Hausdorff".