Ex works at my gym, what should I do?

My boyfriend and I broke up a couple of days ago. Its a long story. Basically he knew he couldn't be with me because of his culture so I broke up with him because he told me that we'd have to break up before one of us fell for the other one. I'm pretty upset at the fact that he still went through with the relationship and didn't even explain to me that we couldn't be together in the long run. I told him that I didn't want to talk to him or see him. He got pretty upset about it and kept begging me to not cut him out of my life. I feel like the best way for me to get over him is to not talk to him right now. I feel like if we talked then I'd still continue to fall for him like nothing happened. Anyways he works at the gym that I go to. I told him that I was going to continue to go but that I'd appreciate it if he acted like I wasn't there. Every time I go there he doesn't talk to me but still stares at me and walks around looking sad. He told me that I'm the coolest girl that he knows and that he doesn't want to ever loose me. I'm not sure if talking to him is going to make me feel better or not. What should I do? And is still going to the gym a good idea?
Ex works at my gym, what should I do?
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