What does it mean when she ask for space? In my opinion, when a girl asks for space this usually means that she has made a decision to move on but is not sure enough about that decision to make it a final break up. Basically, she needs space to see if she can be without you. It could also be that she is having a lot going on and needs to get some things together as well, but ultimately that means that it was not the right timing to get in a relationship.
Rule of thumb, if she ask you for space then give it to her and get busy trying to get over her.