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).
I 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.
