Compact subset

A compact subset is like a tiny little group of things that has some special properties. Imagine you have a toy box with a bunch of toys in it, and you pick out a few of your favorite toys to play with. Those toys you picked are like a compact subset of the toy box.

Now here's the cool part - if you try to cover up all of the toys you chose with a blanket, you might find that no matter how you move the blanket around, there's always a part of a toy peeking out from underneath. That's kind of like the special property of a compact subset - no matter how you try to cover it up, there's always some part that's still showing.

But wait, there's more! If you add up all the sizes of the toys in your little group, you might find that the total is less than some other number (for example, the size of the entire toy box!) That's another neat property of a compact subset - you can add up all the things in it and still get a smaller number than if you tried to add up everything in the bigger group.

So in summary, a compact subset is like a tiny little group of toys (or things) that always has some part showing and can be added up to a smaller number than the bigger group. Cool, huh?