Alexandroff extension

Okay, let's say you have a line and you want to add some points to it to make it longer. The Alexandroff extension is like taking that line and adding a point to each end of it.

But it's not just any point - these are special points called "ends" that don't behave like the regular points on the line. They're kind of like the edges of the line, and they help us understand the line better.

When we add these ends to the line, we get something called the Alexandroff compactification. This is like making the line into a circle, where the ends meet at a point.

So basically, the Alexandroff extension is like adding ends to a line to make it into a circle, and it helps us better understand the line and the way it behaves.