I see on the webpage of a high school math summer program, SuMac, that they will cover some algebraic topology in a period of several weeks. And they covered every aspect of this subject, including Homology, Homotopy, Cohomology and so on.
I am a bit curious about how this is actually done in practice. After all, almost all algebraic topology texts assume quite a bit of knowledge about topologic and metric spaces. There are a lot of theorems and proofs to do even before starting algebraic topology.
Does anyone know why they are soooo efficient in teaching such difficult contents?