Hilbert Curves and Infinite Knots






Jean-François COLONNA

www.lactamme.polytechnique.fr

jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, 91120 Palaiseau, France

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In the year 1890 Giuseppe Peano discovered curves that are going through all the points of a square (and of a cube) showing then continuous surjections between [0,1] and [0,1]x[0,1] (and [0,1]x[0,1]x[0,1]). During the following years, David Hilbert defined more such curves that can be generalized.


Copyright © Jean-François Colonna, 2022-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2022-2023.