Base (topology)

Hey kiddo, do you remember when we talked about shapes and how we can measure them with numbers? Well, topologists are like cool mathematicians who study shapes too, but they use a special way to describe how similar or different two shapes are.

One important thing in topology is called a base. A base is kind of like a superhero cape that helps us see the important parts of a shape.

Let's imagine we have a big shape, like a donut. That's a tough shape to describe with only one number, right? Instead, we can use a base to help us.

A base is like a set of special building blocks that we can use to make the bigger shape. So, for example, a base for our donut shape might be a circle and a cylinder. Those are simpler shapes that we can use to build the donut.

The cool thing about bases is that they help us see similarities between shapes, even if the shapes themselves look very different. For example, if we have a shape that looks like a pyramid, we might be able to use the same base (like a triangle) to build it as we did with the donut.

So, a base in topology is kind of like a special tool that helps us see the important parts of a shape and compare shapes to each other.