Proximity space

A proximity space is like a game of "hot and cold." Imagine you're looking for a toy in your room, and your mom tells you if you're getting closer or further away when you search.

In a proximity space, we have a set of points (like toys in your room), and we want to figure out which ones are close to each other. To do this, we use a function that tells us if two points are close or far apart.

Just like when you're playing "hot and cold," we can use this function to help us get closer and closer to the points that are close together. We can also use it to see if any two points are actually the same point (like when you find the toy you're looking for!).

Proximity spaces are important because they help us understand how things are related to each other, and how we can group things together based on how close they are. They're used in lots of different areas of math and science, from computer science to physics!