Cone (topology)

Okay kiddo, imagine you have an ice cream cone. You know how the top of the cone is pointy and the bottom is wider? That's kind of what a mathematical cone looks like, but instead of ice cream, it's made up of points and lines.

In topology, a cone is a shape that is made up of a base (the wider part) and a point at the top (the pointy part). But here's the tricky part – the edges of the cone are kind of squishy. That means you can bend and stretch them, but they still stay connected.

Now imagine you have a bunch of cones that are all smushed together. They might look like a big mess, but if you zoom in really closely, you'll see that each cone is still connected to the others through their squishy edges.

That's basically what a cone looks like in topology. It's a space made up of points, lines, and squishy edges that connect everything together. And just like with our ice cream cone, the cone in topology has a pointy top and a wider base.

But here's where it gets even more complicated – mathematicians can take this cone shape and squish it in different ways to create new shapes. They might slop the top over to one side or twist the edges around.

The cool thing is that no matter how they squish it, the cone is still a cone in topology. That's because as long as everything is still connected through the squishy edges, it's all part of the same cone shape.

So now you know that a mathematical cone is a shape with a pointy top, a wider base, and squishy edges that connect everything together. And even though it can be squished and stretched in different ways, it's still a cone as long as everything stays connected.