Hemicontinuity

Okay buddy, so imagine you have a line with a bunch of numbers on it. Hemicontinuity is a way of looking at this line to see if it's kinda like a tiny little step ladder, where the steps are getting closer and closer together.

Basically, hemicontinuity says that if you get really close to one point on the line, the numbers on the line will also get really close to that same point. But, sometimes there's a small chance that the numbers might jump to a completely different point, kind of like hopping over a missing step on the ladder.

So, hemicontinuity means things are mostly continuous or smooth, but sometimes there are tiny little jumps that happen. It's sort of like walking up a step ladder, where you might occasionally trip on a missing step and have to hop over it to keep going.