Convergence space

Okay kiddo, have you ever played with Legos before? Imagine you have a big pile of Legos and you want to build a castle. You start by putting the bottom layer of Legos down, then you put more layers on top until you have a big, strong castle.

Now, think of a convergence space like a castle made out of Legos. Instead of Legos, we have sets and points. And instead of layers, we have neighborhoods. A neighborhood is a fancy way of saying a set that contains a point and all the points that are very close to it.

Here's where it gets a little trickier. In a convergence space, we think about sets and points that are very close to each other. Like how the Legos fit together to make a strong castle, the sets and points in a convergence space fit together in a way that helps us understand how things come together.

So, just like how you build a big, strong castle out of Legos, in a convergence space, we use neighborhoods to build stronger and stronger sets that help us understand how different points fit together.

I hope that helps you understand what a convergence space is! It's like building a Lego castle, but with math instead of toys.