Metric Structures in Differential Geometry (Graduate Texts in Mathematics Vol.224) (2004. VIII, 226 p. w. 15 figs. 24 cm)

They are first told that these are derivations on certain equiv­ alence classes of functions, but later that the tangent space of ffi.n is "the same" n as ffi. We have tried to keep these spaces separate and to carefully explain how a vector space E is canonically isomorphic to its tangent space at a point.