ELI5: Explain Like I'm 5

Partially ordered space

Imagine you have a bunch of toys and you want to put them in order. You might start by sorting them according to their size - the biggest toys go first and the smallest go last. This is like a partially ordered space.

In a partially ordered space, you have a bunch of things (like our toys) and you can compare them to see which come before and after others (like sorting by size). However, sometimes it's not clear whether one thing comes before or after another, like with two toys that are the same size - it doesn't really matter which one goes first. So in a partially ordered space, some things may not be directly comparable to others.

Another example could be a set of numbers. We can say that 1 comes before 2, which comes before 3, and so on. However, it's not clear which comes first between 1 and 2. They are related, but not in a clear before-and-after way.

Overall, a partially ordered space is a way of organizing things where some are directly comparable, but others may not be.