Closure (topology)

Imagine you have a box of toys with a lid. When you close the lid, all the toys inside are hidden and cannot be seen from outside the box. This is similar to closure in topology.

In topology, closure is like putting a lid on a set of points on a surface. When we apply closure to a set of points, we are "closing off" any points that are outside the set. This means that if we have a set of points, say a circle, and we apply closure to it, we will get a bigger set that includes the circle and all the points inside it.

To put it simpler, closure means taking a set of points and adding all the points that are "close" to them. Just like closing a box of toys involves adding a lid to it, adding closure to a set of points involves adding any other points that were missing to make the set complete.