Surjunctivity for Cellular Automata in Besicovitch Spaces
Silvio Capobianco
The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behavior of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product topology; in particular, injectivity implies surjectivity.