Is it possible for a function to be separated into two regions of the plane such that a bijection exists between those two regions. In other words, can we separate a curve described by a function into two distinct parts and equate those parts as being equal in size?
I would like to set up a bijection between a curve contained in the unit square, and a curve greater than $1$ in it's domain and range. These curves must be part of the same function but separated like so.
Is there a bijection between these two parts of the function?