End (topology)
An end in topology is kind of like a way of seeing how far away a point is from the rest of the space. Imagine you have a big piece of paper and you draw a dot on it. That dot is like a point in space. Now imagine you draw lots of other dots all over the paper, but you don't want any of them to be too close to the first dot.
You might draw a circle around the first dot and say that any other dot that is outside the circle is really far away. But what if you drew a bigger circle around the first circle, and said that any dots outside of that one were even farther away? You could keep going and draw bigger and bigger circles, each one saying that anything outside of it is even farther away.
Eventually, you might notice that there are no more circles you can draw that really push the other dots away. When you get to that point, you've found an end in the space. It's like a limit to how far away things can be.
Ends can help us understand how a space behaves overall. If it has lots of ends, it might be really spread out and hard to understand. But if it only has one end, we can start to get a sense of how things in the space relate to each other.
You might draw a circle around the first dot and say that any other dot that is outside the circle is really far away. But what if you drew a bigger circle around the first circle, and said that any dots outside of that one were even farther away? You could keep going and draw bigger and bigger circles, each one saying that anything outside of it is even farther away.
Eventually, you might notice that there are no more circles you can draw that really push the other dots away. When you get to that point, you've found an end in the space. It's like a limit to how far away things can be.
Ends can help us understand how a space behaves overall. If it has lots of ends, it might be really spread out and hard to understand. But if it only has one end, we can start to get a sense of how things in the space relate to each other.