have continuous partial derivatives of order "k". If "k" = 0, we only require that the transition maps are continuous, consequently a "C"0-atlas is simply another way to define a topological manifold. If "k" = ∞, derivatives of all orders must be continuous. A family of "C""k"-compatible charts covering the whole manifold is a "C""k"-atlas defining a "C""k" differential manifold. Two atlases are "C""k"-equivalent if the union of their sets of charts forms a "C""k"-atlas. In particular, a "C""k"-atlas that is "C"0-compatible with a "C"0-atlas that defines a topological manifold is said to determine a "C""k" differential structure on the topological manifold. The "C""k" equivalence classes of such atlases are the distinct "C""k" differential structures of the manifold. Each distinct differential structure is determined by a unique maximal atlas, which is simply the union of all atlases in the equivalence class.