Boundary (topology)

Imagine you have a big toy box filled with all sorts of toys. You could split the toys up into two groups, ones that are inside the toy box and ones that are outside the toy box. The line that separates these two groups is called a boundary.

In math, we can think of shapes and spaces that are like the toy box, and the boundary is the line that separates what's inside from what's outside. But we have to be careful, because sometimes the boundary of a shape might not be a line, it might be a point or even an entire surface (imagine a ball where the entire outside surface is the boundary).

So when we talk about the boundary of a shape or space in math, we're talking about the part that separates what's inside from what's outside.