I was just sitting at the mall taking a break from mall walking. A man walked over to me when I wasn’t even looking up. He said "I haven’t seen you here before. " I said I wasn’t really here to talk to people and got up and walked away. He said he would leave, he may even have said sorry. I said I was ready to leave anyway. In retrospect I think he may have just been slightly mentally challenged so I wish I had been a little softer, he did not turn out to be aggressive. Looking for suggestions on something still clear and firm but more polite? This scared me for some reason, I think how fast he walked up and sat down near me.
Editing to add a key detail, he sat down close to me which is probably what made me more nervous than I would have otherwise been. I appreciate all the thoughtful feedback I’ve gotten and interesting discussion.
I don’t directly know OP’s age or the man’s age in this case, but I’m giving OP the benefit of the doubt, and from context I’m inferring that the man was probably older than her given that she refers to him as a “man” and it just sounds like she’s relatively younger (especially if this is sort of one of her first experiences with this sort of thing).
The “sat down close to me” also makes it sound like there was sufficient open seating, and the man specifically chose to sit directly next to and close to this girl. I understand that public spaces often have inadequate seating options and seats that are packed too close together for comfort, and that’s a separate problem, but there’s nothing suggesting that’s what actually happened here, and as I said, I am giving OP the benefit of the doubt.
With those contextual details in place, in my world and perspective, I would suggest that the older man approaching the younger girl to talk should probably approach with some caution, not “fast”, and perhaps even ask permission before sitting and trying to strike up a conversation. I don’t think that’s unreasonable or too much to ask. I’m not saying anyone can’t strike up a conversation with anyone they choose to, of any age, but for the people that choose to do so with strangers, they would benefit from having some social awareness if the situation is anything like what I am picturing (unfortunately realistically) in my head.