Completely uniformizable space

Okay, imagine you have a toy room with different toys placed all over the room. Sometimes you may want to play with the toys that are very close to each other, and sometimes you want to play with the toys that are further apart. In order to do that, you need a clear path to get to each toy without obstacles in your way.

Now imagine a space where there are no physical toys but instead there are invisible points. When we talk about a completely uniformizable space, we are saying that this space has a special property where we can clearly see a path to get from one point to another point without any obstacles in the way.

This property is important because it helps us to understand how things move and behave in that space. We can always see our way around, and we don't have to worry about getting stuck or going the wrong direction. It makes it easier to study and work with this space because we can clearly see how everything is connected through these paths.

So, in short, a completely uniformizable space is like a toy room without any obstacles that helps us understand how everything in that space is connected.