Solution
= Solution
A point $x\in X$ is critical if $df_x:T_xX\to T_{f(x)}Y$ is not surjective. A critical value is an image of a <critical point>; a <regular value> is a point $y\in Y$ for which every point of $f^{-1}(y)$ is regular, including vacuously values with empty preimage. <Sard theorem> says that for a smooth map of finite-dimensional manifolds, the critical values have measure zero in every coordinate chart of the target. In particular regular values are dense.