ELI5: Explain Like I'm 5

Urysohn universal space

Have you ever played with a toy box that had different shapes that fit into each other? For example, maybe there was a triangle that fit inside of a square, and then that square fit inside of a circle.

Well, mathematicians have a similar idea with something called a Urysohn Universal Space. It's a special kind of mathematical space that can fit inside of lots of other spaces.

Imagine you have a room with lots of furniture in it - a couch over here, a table over there. You want to be able to move around the room and see everything from different angles.

But what if you could shrink yourself down really small and crawl into that same room? You could move around and see everything from a totally different perspective.

That's kind of what a Urysohn Universal Space does. It's a special mathematical space that is really flexible and can fit into lots of different shapes and sizes. Just like you can crawl into a room and see it from a different perspective, mathematicians can use a Urysohn Universal Space to help understand other shapes and spaces in the world of math.

Think about it like a puzzle piece that fits into lots of different puzzles - it helps mathematicians put their ideas together in new and creative ways. So even though it might seem complicated, a Urysohn Universal Space is really just a flexible tool that helps mathematicians explore the world of shapes and spaces.