Totally bounded space

Okay kiddo, let me explain what a totally bounded space is. Imagine you have a big, big playground full of toys - balls, cars, dolls, you name it. Now imagine you want to put all those toys into a small ride-along toy wagon.

A totally bounded space is a lot like that wagon. It's a special kind of space where you can fit all the points in the space into a small box or container. Just like all the toys fit into the wagon. But, here's the tricky part, no matter how many times you divide the space into smaller chunks, you can always find a box or container that will fit all the points in that chunk.

So, it's like you have a big group of friends, but you can always find a small enough car to fit all of them inside. This is called being totally bounded.

Now, why is this important? Well, it's used a lot in math and science to help study different kinds of spaces. And, just like how a well-packed wagon or car can help you take all your toys or friends to a new place, knowing that a space is totally bounded can help us move around and understand it better.

I hope that makes sense, kiddo!