FYI for Americans: when you describe pizza as pie and non-American English speakers are listening, their inner child recoils in horror. pizza = flat thing with cheese on top, pizza base at bottom pie = closed thing with significant vertical component, pastry on top and bottom Otherwise, every flatbread or similar thing on earth is a pie. Observe: "Oh, I really dig these Indian roti -pies". "Pass me another naan -pie"…
Second, a pie needn't have pastry on both top and bottom. There are numerous pies with no crust on top, such as pumpkin pie, key lime pie, banana cream pie, lemon meringue pie, chess pie, pecan pie, or chocolate icebox pie. These are so similar to pies with crust on top that it is hard to see how a reasonable definition could include one but not the other.