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I have seen a couple ways to assign meaning to the words "one and a half dimensional" and neither of them are actual spaces (i.e. have a basis, are full of vect
by whatshisface 5y ago
I have seen a couple ways to assign meaning to the words "one and a half dimensional" and neither of them are actual spaces (i.e. have a basis, are full of vectors).
- eru 5y agoCompare https://math.stackexchange.com/questions/1466820/vector-spaces-with-fractional-dimension https://math.stackexchange.com/questions/1466820/vector-spac... and perhaps https://faculty.math.illinois.edu/~reznick/CantorSetArithmetic.pdf https://faculty.math.illinois.edu/~reznick/CantorSetArithmet... https://www.princeton.edu/~fhs/fhspapers/fhspaper91.pdf https://www.princeton.edu/~fhs/fhspapers/fhspaper91.pdf might come closer?
- whatshisface 5y agoI don't understand the first one, the second one isn't about continuous spaces (cantor dust has gaps), but the last one seems pretty interesting and I'm working through it. Thanks for the links! Edit: The last paper only describes fractional dimensions in a limited sense, because the way the author constructs the coordinate system still involves a positive integer number of coordinates.