Cellular Automata in the Cantor, Besicovitch, and Weyl Topological Spaces
François Blanchard
Institut de Mathématiques de Luminy - CNRS,
Case 930, 163 avenue de Luminy,
F-13288 Marseille cedex 09, France
Enrico Formenti
Laboratoire de l'Informatique du Parallélisme,
Ecole Normale Supérieure de Lyon,
46 Allée d'Italie,
F-69364 Lyon cedex 07, France
Petr Kůrka
Faculty of Mathematics and Physics,
Charles University in Prague,
Malostranské nám. 25,
CZ-11800 Praha 1, Czechia
Abstract
The Besicovitch and Weyl pseudometrics on the space 
of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from by factoring through the equivalence of zero distance. Cellular automata are considered as dynamical systems on the Besicovitch and Weyl spaces and their topological and dynamical properties are compared with those they possess in the Cantor space.
