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==Notes== {{Reflist |group=notes |refs= <ref name="space filling note">The Hilbert curve map is not a [[homeomorphism]], so it does not preserve topological dimension. The topological dimension and Hausdorff dimension of the image of the Hilbert map in '''R'''<sup>2</sup> are both 2. Note, however, that the topological dimension of the ''graph'' of the Hilbert map (a set in '''R'''<sup>3</sup>) is 1.</ref> <ref name="levy note">The original paper, {{cite journal|last=Lévy |first=Paul |title=Les Courbes planes ou gauches et les surfaces composées de parties semblables au tout |journal=Journal de l'École Polytechnique |year=1938 |pages=227–247, 249–291 }}, is translated in [[#classics|Edgar]], pages 181–239.</ref> }}
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