Advice on breakup please?

My boyfriend recently cheated on me and had also been talking to other girls. 3 days ago I broke up with him after finding out he’d been messaging other girls again. Now I know the advice is going to be telling me not to get back with him etc, but I do love him and miss him. Do you think I should message him just to see if it’s completely over? I feel I need to know almost for my own closure if so because currently I’m constantly wondering what if he comes back to me and I’d rather just know so that I can properly move on if not.
Advice on breakup please?
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