My ex wants to be friends?

We broke up a last week and she said she'd really like to be friends still....but the thing is I'm still strongly infatuated with her/love her. She didn't give me a good reason for breaking up, so I don't know if she still likes me or not. I don't know whether to stay friends or just end it all together... I want to ask her if she could reject me properly like "I don't like you, I never will." or something like that. Should I?