I am looking for the theorem which states that a bijection from a set of infinite measure to one of finite measure will always "compress" the infinite set near the boundaries of the finite one. Basically, if you were to squeeze the [infinite] universe into a tennis ball, more "universe" would end up clustered near the surface of the ball than at the center, regardless of how you orient the ball or deform the universe inside it.
I'm not sure what to tag this as since the idea can be formalised using metrics, order, topology, calculus, or any of several combinations thereof. I remember seeing this theorem in the context of real analysis (the topic was functions $\Bbb{R}\to (-L,L):L\in\Bbb{R}$), but I don't remember what it was called.
Example:
The Riemann sphere and other stereographic projections provide a convenient example. In this case, it is best to think of the sphere as the quotient of a disk whose radius is finite (e.g. the unit disk) and the pole (point at $\infty$) as the boundary of this disk.
Notice that the points on the Riemann sphere "cluster" towards the pole and that, when projected to the Riemann sphere, any continuous transformation of the complex plane still has a pole where the points become "infinitely dense".