I am not even convinced that the function is from the reals to the reals:
It might be a strange field, like it could be the complex numbers, or even the pAdic's, where the notion of "distance" and closeness gets weird.
Rene Thom's catastrophe theory tried to model this, but was not strong enough.
http://en.wikipedia.org/wiki/Catastrophe_theory
It might be a strange field, like it could be the complex numbers, or even the pAdic's, where the notion of "distance" and closeness gets weird.
Rene Thom's catastrophe theory tried to model this, but was not strong enough.
http://en.wikipedia.org/wiki/Catastrophe_theory