Topological dimension

Imagine you have a bunch of toys, like blocks or Legos. You can put them together in different ways to make shapes. Some shapes might be flat, like a circle or a square, and some might be bumpy or have lots of corners, like a star or a pyramid.

Topological dimension is a way to describe how complex a shape is, based on how many directions you can move in without changing where you are.

For example, a flat shape like a circle is 1-dimensional, because you can move around the edge of the circle in one direction. A square is also 1-dimensional, because you can move around the edge in one direction. But if you have a bumpy shape like a star, you might be able to move in more than one direction without changing where you are.

In math, we use topological dimension to describe shapes that might be very complicated, with lots of bumps and twists and turns. For these shapes, it's not always easy to say how many dimensions they have just by looking at them. But by using topological dimension, we can always find a way to describe them in a clear and simple way.