Please Help. I feel like I am in hell. In our Topology class we defined homology via a bunch of Axioms - however it was quite confusing and so I now wanted read about it in a book. The problem now is, we didn't define/use the "Eilenberg Steenrod axioms" which define a homology theory as a functor on category pairs of topological spaces. We defined a homology theory as a functor simply on the category of topological spaces and instead of the excision axiom we required our border map to make the Mayer-Vietoris Sequence exact. AI told me that these definitions are equivalent and that this was a well known fact, but even after spending several hours(!!) trying to find this other definition in a book, all I could find what this very vague Answer on Math overflow. https://mathoverflow.net/a/97647
Can anyone help? Is there any source that provides greater detail on this?
