the principle is this: without any additional structure, unlabeled points are not the lattice Z^n. They are a Z^n-torsor. You need a little extra structure in order for the space to be separated (Uausdorrf). the point might say "well, if you see exactly the same thing as me..
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...but then I've never known where 'one is': and I've yet to meet somebody or something that does! As for 'realizable': that's a very peculiar something that we try and measure and appears much to do with the hall of mirrors which is 'experience'.
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