Čech closure operator

Okay kiddo, imagine you have a bunch of toys in your room. You can group them together based on how similar they are, like all the dolls in one corner and all the cars in another corner.

Now let's say someone gives you a new toy and you're not sure where it belongs. You can use the Čech closure operator to figure it out. Basically, you grab the new toy and put it in a group with the toys that it is most similar to.

Then you look at the other groups and see if any of them are close enough to the new group that you can combine them. You keep doing this until you can't combine any more groups.

So in your room, you might put the new toy with the dolls at first. Then you see that there are some stuffed animals that are similar enough, so you combine those groups. Then you realize that some of the cars are also similar enough, so you combine those groups.

Now you have a bunch of groups of toys that are all similar to each other, and the new toy is in the group where it fits best. That's the Čech closure operator!