So, I'm trying to solve an exercise and among the given facts there is the following claim:
Let $y_0 \ge 0$ such that the intersection between $\{y=y_0\}$ and $\{f(x,y)=h(y)\}$ is transversal $(*)$
Note that $f \in L^\infty(\Omega \times [0,+\infty))$ and $\Omega$ is a compact manifold in $\mathbb R^2$. About $h$ we only know that is a well defined function.
QUESTION: What information -regarding $h$ or in general- can we obtain from $(*)$?
To be honest, is the first time I hear the term "transversality". Although I found some definitions concerning manifolds and their tangential maps, I'm not able to find the relation between them and my claim (if there is such one). What does $(*)$ imply?
I apologize if my question is a bit blurry but I'm having a really hard time understanding what should $(*)$ yield.
Any help is much appreciated. Thanks in advance!