Holomorphically convex hull

Imagine you have a big basket and inside the basket are lots of toys. Some toys you can see and some you can't since they are hiding behind other toys in the basket. But you really want to know where all the toys are so you need to find a way to figure it out.

In math, sometimes we have a similar problem. We have a big area called a set and inside the set are lots of points. Some points we can see and some we can't see since they are hiding behind other points in the set. But we really want to know where all the points are so we need to find a way to figure it out.

This is where the holomorphically convex hull comes in. The hull is like a special tool that we can use to find all of the points. We use special math rules called holomorphic functions that help us see all of the points in the set.

To understand this, think about the different parts of your body like your eyes, nose, mouth, and ears. Each one serves a different purpose and helps you understand things in different ways. In math, holomorphic functions are like different parts of our body that help us see things from different angles.

So when we use the holomorphically convex hull, we are gathering up all the information we can about the set by using these special holomorphic functions. We are then using this information to make a shape around all of the points in the set, kind of like putting a fence around all the toys in your toy basket.

The holomorphically convex hull gives us a clearer picture of the set by showing us all the points hiding behind other points. It's like having superpowers and being able to see through walls and objects to find what you're looking for.