A Mean Customer

I guess every now and then we meet up with mean and inconsiderate customers. I mean I try not to get upset with people when they say things out of ignorance. But ya'll I end up having an arguement with one. This particular customer came by after shop hours, actually in fact I was already closed. I have my close sign up on the door too in big bold CAPITOL letters. This customer just wanted to simply ignore this and have his way and still wanted to open up.

Me: I'm closed.
customer: Well I'm here now, you can still open and let me buy something.
Me: No, I'm closed.
customer: You ain't that busy that you have to be close.
Me: Don't tell me whether I'm busy or not, it's none of your business what I do.

See this is the thing everybody, it was the principle of the fact that when I say I'm closed, and just because this customer stopped by I was suppose to open up the shop for that customer. This customer wanted their own way, and wanted me to open up whenever they came. It didn't matter when I was closed. Well do I ban this customer from my premises? It's just the principle of the whole thing of consideration. I really don't want to serve this person anymore.
It really ticked me off also because they even had the nerve to try to put me dow and degrade me. I was furious. I'm going to be opening an online store soon. This incident has
really motivated me to move forward to do that, full speed ahead. Dealing with customers can be really a pain. At least with an online store, If there are any meanies, I don't have to deal with them face to face.

So I need some advice, do I ban this customer from premise, or do I firmly lay down the law. I really don't want to deal with this customer again.

Peace and Love