Core-compact space

Okay kiddo, so imagine you and your friends are playing a game of hide-and-seek in a really big room. The room has a lot of furniture and things in it, but you still want to hide somewhere where no one will find you.

Now, let's pretend that the room has a special rule – if you hide in a certain part of the room called the "core" then you are automatically safe from being found.

But wait, there's more! The room also has another special rule – if you try to move the furniture around in such a way that there is no longer a way to get to the core, then your friends cannot play hide-and-seek anymore.

So, in math terms, we say that the room is a "core-compact space." A space is core-compact if it has a special part called the "core" that is protected from being found (like the safe spot in hide-and-seek), and is also compact (which means you can't change the layout of the room too much or it stops working).

I hope that makes sense, kiddo! Just remember that a core-compact space is like a big room with a special part that's super safe, but you can't mess with the layout too much!