The diversity of cyberworlds makes it hard to see consistency in terms of invariants. The consistency requires for us to abstract the most essentials out of the diversity, and hence the most abstract mathematics. It has been true in science in general, and in the theory of universe in particular. What are the most essential invariants in modeling cyberworlds? A branch of the most abstract mathematics is topology. For topology to be computable, it has to be algebraic. So, the searches have been for over two decades in algebraic topology for cyberworld invariants. Equivalence relations define invariants at various abstraction levels. The paper solely serves as an initial summary of algebraic topological resources for studying cyberworlds starting from the very elementary set theoretical level. High social impact application cases of e-financing and e-manufacturing are presented at the end.