Compact submanifold
Have you ever played with play dough? Imagine you have a big ball of play dough, and you squish it down until it becomes a smaller ball. Now imagine that the big ball is like a gigantic space, and the smaller ball is a special shape that can be found inside that space.
That special shape is called a submanifold, and if it's even smaller and squished up really tight, we call it a compact submanifold.
But it's not just any random shape - it has to follow some rules. For example, it has to be smooth and have a certain number of dimensions (just like how a line only has one dimension, and a square has two dimensions).
So imagine a tiny little shape, like a point or a line or a circle, that follows all these rules and lives inside a really big space. That's a compact submanifold!
That special shape is called a submanifold, and if it's even smaller and squished up really tight, we call it a compact submanifold.
But it's not just any random shape - it has to follow some rules. For example, it has to be smooth and have a certain number of dimensions (just like how a line only has one dimension, and a square has two dimensions).
So imagine a tiny little shape, like a point or a line or a circle, that follows all these rules and lives inside a really big space. That's a compact submanifold!