I looked over the explanation on the Wiki and, thinking about it, I'd say that the surface around the tip of Norton's Dome is not a continuous function, which a

I looked over the explanation on the Wiki and, thinking about it, I'd say that the surface around the tip of Norton's Dome is not a continuous function, which alone is enough for me to disqualify it. Intuitively, that's a sufficient explanation to me, or at least a sufficient start of one. IANAPhysicist, so I'll ask here: are there any examples of surfaces or phenomena in classical physics that are defined by a discontinuous function, and are something you'd actually expect to see existing in the real world? Things seemingly discontinuous until you zoom in close enough don't qualify.