Suspension (topology)

So imagine you have a big, bouncy ball. And you have a bunch of strings attached to it that are holding it up in the air. Each string is connected to a point on the ball, and all the strings together are holding the ball in place.

Now think of a city with a lot of buildings and roads. Each building and each road is like a point on the ball, and the strings are like the connections between those points. But instead of holding up a ball, they're holding up the structure of the city.

That's kind of what we mean when we talk about suspension in topology. It's a way to connect all the points in a space (like a city or a ball) so we can study the whole thing together as a cohesive unit.

Why is that useful? Well, it helps us understand the properties of the space we're studying. For example, we might be interested in whether it's possible to draw a path from one point to another without going through a certain other point. By looking at the way all the points are connected, we can answer that question more easily.

So when we talk about suspension in topology, we're really just talking about the way we connect all the points in a space so we can understand it better. And just like with the bouncy ball, it's all about the connections between the points!