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I want to ask a problem from Lee ' s book Introduction to Smooth Manifolds: Let F_p denote the subspace of C^\inf(M) consisting of smooth functions that vanish at p and let F^2_p be the subspace of F_p spanned by functions fg for some f,g \in F_p. Define a map \phi: F_p-----> (T_p(M))^star by f-----> df_p Show that F_p/F^2_p is isomorphic to (T_p(M))^star

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