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    \textbf{ MATH534A, Problem Set 2, due Sep 8}
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    All problems are worth the same number of points.
    \begin{enumerate}
    \item Show that for two smooth atlases the set of smooth functions is the same (i.e. a function is smooth w.r.t. one atlas iff it is smooth w.r.t. the other one) if and only if the union of those atlases is a smooth atlas.
    \item Problem 1-7 from the textbook.
    \item Problem 1-9 from the textbook.
       \item Problem 2-3 from the textbook.
              \item Problem 2-11 from the textbook.
    \end{enumerate}
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