I thought it was quite strange myself, with it being crooked. But I thought the top was strange also because it looks to have been broken... but I'm not sure if it has been, because I've seen bottles with the jagged edge looking top before... hmm, I'm just not sure.
My first thought was a syrup dispenser for soda fountain, but the base starburst was common on the perfume & cologne bots....but would explain the top, which would have had a metal dispenser type top. Also seems a bit large for a perfume and fat for olive oil.....just my thoughts to confuse anyone.....Jack
You might want to clean it up a bit more.
It sounds like your talking about a ground top which should have had a metal cap as well. The outside looks like it has a berm rising from the edge, the inside of the neck looks ground to fit a glass stopper which makes no sense at all. Very puzzling to me but I don't have it in hand and the Foreign made bottles have never been something I get exposed to.
Is it a little wider than deep or just round? I get that impression from the pictures.
It's a bit tall for an atomizer but maybe a hair tonic shaker?
Oh heck, I'll stick with oil or ink. Either of them could have had a "pour in small quantity" top too.