Relatively compact subspace

Okay, kiddo! So, remember when we talked about sets? A set is just a bunch of things grouped together.

Now, let's talk about subspaces. A subspace is just a special type of set. It's a part of a bigger set that is also a set on its own. It's kind of like a smaller box that fits inside a bigger box, but both are still boxes.

When we say "relatively compact subspace," it means that this smaller box is not too big, even though it's inside the bigger box. It's like having a small toy car inside a big toy truck. Even though the toy truck is much bigger, the toy car still fits inside nicely because it's relatively compact.

So, when we talk about a relatively compact subspace in math, we're essentially saying that it's a part of a bigger set that is small enough to fit inside, but is still its own set.