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Around 1998, I encountered a (forgotten) reference to a particularly strange space-filling curve. Consider a foliation as a collection of continuous nonintersecting curves that start at $(0,0)$ and ...

There is a surjective continuous map $[0;1]\rightarrow [0;1]^2$ ("space filling curve"). Using such a map one can easily get space filling curves for all finite dimensional cubes. So my question is: ...