Talk:Preimage Theorem

As stated, the theorem is nonsense, since a submersion can only have regular values. I suggest the following wording: "Let $\varphi \colon M \to N$ be a smooth map between the smooth manifolds $M,N$ and let $y \in N$ be a regular value of $\varphi$. Then the preimage $\varphi^{-1}(y)$ together with the natural inclusion $\iota:\varphi^{-1}(y) \to M$ is an embedded smooth submanifold of $M$ of dimension $\dim M - \dim N$." --Geometry dude (talk) 00:08, 6 September 2014 (UTC)