My boyfriend needs space to clean up his old relationship... I'm in fear
	
	
		I am in a relationship for 2 months. I entered this relationship with a little complication. He told me that he left his girlfriend 7 months prior to us meeting. However she still holds the keys to his apartment. She goes there whenever. Nonetheless, he talks to me 24/7 even when she is there. At one time while I was on the phone with him, I heard him telling her that he is on the phone with his woman and she needs to move on just the same. He is always at my house. Many times he assures me that he is not involve with her. I truly believe him but the problem I am having is that why is she still there. When I asked him, he said if I should know the real reason he would have to discuss the entire detail of the relationship, which he does not agree with. I am now overwhelm with the situation and since now I am asking a lot about her. I told him recently that after July month end I will not continue in such situation. So he says since I can't deal with her being there and trusting him, then I should give him the time to clean up his mess and he is fearful that he will lose me which he really does not want. He says I am is everything and he needs me. He is also suggesting that we slow things down a bit. I am now concern and anxious since I was the one who gave the ultimatum. I am fearful of losing him too. 
What does giving space includes... do people still be invovled while there is space? 
Please respond I need clarification. Is this the man for me?