Just briefly skimming over your post, a quick correction to the Continuity section: > Definition (Homomorphism) There is a homomorphism (i.e. an equivalence re

Just briefly skimming over your post, a quick correction to the Continuity section: > Definition (Homomorphism) There is a homomorphism (i.e. an equivalence relation) between two topological spaces if there exists a function f:X→Y, where X and Y are topological spaces (X,τX) and (Y,τY) with the following properties This should be "homeomorphism", not "homomorphism". A homomorphism is a structure-preserving map, like a continuous function (in the context of topological spaces) or a linear map (in the context of vector spaces). Homomorphisms are very much one-directional. Homeomorphisms, on the other hand, are specifically equivalences between topological spaces, and are defined as continuous functions with continuous inverses. Edit: finished reading it. I'm impressed by how much you cover in such a short space. Overall it looks good, so thanks for taking the time to write it. Some of these ideas are at a pretty high level of abstractness, so I sympathize with anyone who struggles to get any kind of intuition for them at a first go.