Are there any examples other than using dimension for vector spaces where the easiest way to show that two objects are isomorphic is by using a classification theorem and showing that they must both be in the same class? (homeomorphisms count too)
Genus for surfaces would be a simple example.
Connectedness for compact $1$-dimensional manifolds would be another!
Sign up using Google
Sign up using Facebook
Sign up using Stack Exchange
4 years ago