I think I have forgiven someone for betraying me. Yet, I actually do not want to have anything to do with this person anymore. Does this mean I have not forgiven?
We need to make a distinction here between forgiving and reconciling. The late Lewis Smedes, in his 1984 book, Forgive and Forget, made the compelling point that we know we have forgiven someone “if we wish the other well.” If you wish the other well, hoping that bad things do not happen to the person, then you have forgiven.
Forgiveness usually leaves us with some residual feelings of anger or sadness about what happened, but these emotions then are not intense and dominating us. In contrast, reconciliation is when two or more people come together again in mutual trust. Given that you were abandoned, your trust in that relationship likely is low and should be low if the other is continuing the hurtful behavior. So, yes, you very well may have forgiven, but you rightly are not ready to reconcile.