AF algebras can be constructed from matrix algebras by using Bratteli diagrams. By Choi's theorem the pure state space of a matrix algebra is a complex projective space. I am assuming that someone has put these together and given the state space of an AF algebra as a limit (using the Bratteli diagram) of finite dimensional manifolds. I would be very grateful if someone could point me in the right direction to read about this.
This is a specialisation to AF algebras of a question I asked earlier which received 8 upvotes but no comments. I have tried to make it more specific.