been too long since we had a pointless taxonomic dispute HERE'S A POWERPOINT ON WHY A QUESADILLA IS ACTUALLY A PIE
There's plenty of precedent for pies not having tops. Perhaps the most classic and iconic pie, the cream pie that gets thrown in someone's face in a cartoon, after all has no top.
It's cases like these that require a taxonomy not based on which faces of the food item are covered by baked grainmeal, but is rather function-based. Pizza is different from pie because you eat it differently. Hot dogs are (by this argument) a kind of sandwich because you eat them the same way.
