> What most people here apparently think of as a topping, I call a condiment or a garnish. Again, it's a difference of dialect, apparently. I see no reason to use "topping" identically to the other two words and lose its obvious and natural distinction.

If you have to explain your definition of a term to a whole group of people who agree on it meaning something different, then it is neither obvious nor natural.

You can make correct statements out of seemingly incorrect statements by redefining your terms in just the right way, but this doesn't mean your opinion on the actual topic at hand is valid when you redefine the terms used by the question itself so that they mean things that were not intended to mean. In other words, if you want to define the word "topping" to mean something that nobody else in this discussion is defining it to mean, then you can pretty much make any statement you want about it, so long as your redefinition fits just right. But it isn't helpful in reaching a conclusion about the actual idea under discussion. I could define "cheese" to mean "something colored red before cooking" and "topping" to mean "something that came out of a cow" and make all kinds of statements I was previously refuting back when those terms meant what I meant them to mean and everybody else understood them to mean.

What is natural and obvious to me is that a "cheeseburger topping" is something that goes on top of a cheeseburger, and "hamburger topping" is something that goes on top of a hamburger. With these definitions, cheese is potentially a hamburger topping but not a cheeseburger topping. (A respectable yet respectably refuted argument could be made that "extra cheese" could be considered a cheeseburger topping.)

Moreover, since the obvious and natural interpretation of the terms used in the question is more of a human interpretation than a strictly logical interpretation, I reject any notion that the top half of the bun is either a hamburger topping or cheeseburger topping. While technically fitting the terms as I have defined them, it is supremely unhelpful (in this case) to sacrifice what is humanly understandable with a pedantic rejection of the natural assumptions implicit in any question involving elements of the real world.