Homotopy excision theorem
Have you ever tried to paint a picture on a really big canvas, but there was already something on it that you didn't want there? It's hard to ignore that thing and paint what you actually wanted to paint.
The homotopy excision theorem is like a magic eraser for mathematicians. It helps them to ignore some parts of a space and focus on the parts they really care about without getting distracted by things they don't need.
Imagine you have a big shape, like a circle, but you only care about a small part of it, like a tiny dot in the middle. The homotopy excision theorem says that you can just focus on that tiny dot, and everything outside of it won't matter! You can pretend that the rest of the circle doesn't even exist.
This is super useful because sometimes in math we have really complicated shapes with lots of parts we don't care about. The homotopy excision theorem helps us simplify things and focus on what we really need to know.
The homotopy excision theorem is like a magic eraser for mathematicians. It helps them to ignore some parts of a space and focus on the parts they really care about without getting distracted by things they don't need.
Imagine you have a big shape, like a circle, but you only care about a small part of it, like a tiny dot in the middle. The homotopy excision theorem says that you can just focus on that tiny dot, and everything outside of it won't matter! You can pretend that the rest of the circle doesn't even exist.
This is super useful because sometimes in math we have really complicated shapes with lots of parts we don't care about. The homotopy excision theorem helps us simplify things and focus on what we really need to know.