Somewhat simple question, but it's the following. Consider D-volumes (that is, the equivalent volume measurement in D dimensions) of spheres of ever-higher dimensions. The percent of D-volume concentrated in a $\epsilon$ crust around the sphere is
$1-(1-\epsilon)^D$ (This derivation is pretty easy so leaving it out.)
For a given $\epsilon$, this percentage gets much higher as D gets higher.
My question is, I want to say that the 'topology' of spheres changes as you go into higher dimensions. But I know that's not right at all. What is the correct word for the phenomenon I'm describing?