Watch a serious horror flick right before you go to bed. It will cause you to have a nightmare of a different kind. Hopefully, these dreams will ease up soon. It is totally normal to only remember the good parts of a relationship once you break up. It happens with people who are divorcing and who lose someone to death as well. It is simply the grieving process kicking in.
Perhaps, there's residual sentiment... and the unconscious thought of better times and longing for what used to be. The dream state is just a way to process all of that. I suggest that you accept the dreams and resist getting upset over them... after all, these are only dreams. In the fullness of time, his memory and the dreams of him will fade.
I agree with specialmom, it means tht you still have feelings for him, your thinking about him and now dreaming about him. You do not feel closure, but remember that he cheated on you, which means he is high risk for future infidelity with you and probably other women too, so surround yourself with good friends and family and start to rebuild your life again. Yes, you can do it and never stay with someone who does not apprecite you, respect you and the relationship and most of all, someone who is a cheater.
It probably means that you are thinking about him a lot still. That will get better. You need to start getting out there and doing other things that keep you too busy to think about him. Go do things with friends, family, etc. Join a group. Exercise a lot as this makes us feel better as the activity releases our bodies own "happy" chemical.
Sounds to me like this relationship was not great. And you should not want a guy who cheated on you back. You deserve better than that.
So today, stay busy. Tonight, read a book or watch a movie and keep your mind occupied and as you go to sleep think about the movie you just watched, your job, etc. Actively think about something else and your subconscious will follow. But don't believe for a second that this means you should get back together with him. It is a natural thing that happens and goes away. good luck