<human>: Can you condense the text into a few key points?

About 4 months ago my ex (22F) broke up with me (21M) because she didn't feel like it was a good time for her to be in a relationship and because she had some personal issues she wanted to work on. 

We've maintained fairly regular contact since then and have hung out on occasion. All contact has been initiated by her, I haven't done anything really. Lately, I've been increasingly distant and cold to her and I'm starting to feel guilty about it. She moved to my city a month before we broke up and doesn't have many friends here except for a few people from work so she is lonely (she flat out told me she was). The other day she initiated the first real conversation we have had in about a week and it took her about 5 hours to respond to a text of mine so I got angry and just ignored her after that. I get a facebook message from her later saying how its weird that we weren't friends (I deleted her immediately after the break up) anymore. I responded by saying that it was probably for the best and that's it. 

I feel so guilty about being so cold to her. On one hand, I tell myself she is clearly trying to reach out to me and that I should maintain the friendship to keep open the possibility of getting back together in the future. But the other part of me thinks that she is just using me for emotional support and is looking for entertainment when she is bored or lonely. I just can't decide if I should ease up a bit and be a little more friendly to her, not so much as to get back together but not to be a dick. I realize that she isn't entitled to a friendship seeing as how she broke up with me but I can't shake the feeling that I'm being a total asshole here. I'm just afraid that if I keep the friendship alive, I'm only going to get hurt again if she starts seeing someone else. 

Should I ease up a little bit? Should I tell her why I'm acting this way? Does she even deserve to know why?
<bot>: I feel like an asshole for being so cold and distant to my ex who is trying to maintain a friendship. Afraid of being used for emotional support and afraid of getting hurt all over again.