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We bring out some similarities among one-dimensional surjective
cellular automata. Four main results are the following: (i) all
periodic points of a cellular automata are shift-periodic if and
only if the set of periodic points of any fixed period is finite,
(ii) forward recurrent points as well as backward recurrent points
are residual for every onto cellular automata, (iii) every onto
cellular automata is semi-open, and (iv) all transitive cellular
automata are weak mixing and hence maximally sensitive (which
improves an existing result).