TITLE: Example of an open map on $\mathbb{R}^2$ that is not a submersion
QUESTION [6 upvotes]: I am searching for an example of a map $f : \mathbb{R}^2 \to \mathbb{R}$ that is open but is not a submersion... I know that any constant map is not a submersion, but it is indeed closed, I am wondering for an example where $f$ is an open map.
I appreciate any help!

REPLY [8 votes]: Try the map $(x,y) \to x^3.\,\,$