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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 vectordoi:10.1016/j.tcs.2010.09.020 fatcat:2wct3xu6xfbr7mgpgmq3qm4hou