Abstract
When G is an arbitrary group and V is a finite-dimensional vector space, it is known that every bijective linear cellular automaton τ : V G → V G is reversible and that the image of every linear cellular automaton τ : V G → V G is closed in V G for the prodiscrete topology. In this paper, we present a new proof of these two results which is based on the Mittag-Leffler lemma for projective sequences of sets. We also show that if G is a non-periodic group and V is an infinite-dimensional vector space, then there exist a linear cellular automaton τ 1 : V G → V G which is bijective but not reversible and a linear cellular automaton τ 2 : V G → V G whose image is not closed in V G for the prodiscrete topology.
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