The Inverse Function Theorem provides sufficient conditions to determine when a function is defined implicitly by a relation. I would like to know some ways to determine when no such function is defined.
Below is a link to a specific example and conjecture.
http://math.stackexchange.com/questions/46750/how-to-prove-the-implicit-function-theorem-failshttps://math.stackexchange.com/questions/46750/how-to-prove-the-implicit-function-theorem-fails
