Continuity (topology)

Continuity in topology means that if you have two sets of things, and you change one of the things a little bit, then the other set of things will also change a little bit, but they won’t change too much.

For example, imagine you have a line of toy cars, and you’re moving them one by one along the line. If you move a car a little bit to the left, the next car in line will also move a little bit to the left, but not too much. If you move a car a lot to the left, then the next car will also move a lot to the left, but that’s not continuity.

Continuity is when small changes in one set of things cause small changes in another set of things, and big changes cause big changes. It’s like a smooth transition from one set of things to the other, without any sudden jerks or changes.