  For an arbitrary group $G$ and arbitrary set $A$, we define a monoid
structure on the set of all uniformly continuous functions $A^G\to A$ and then
we show that it is naturally isomorphic to the monoid of cellular automata
$\mathrm{CA}(G, A)$. This gives a new equivalent definition of a cellular
automaton over the group $G$ with alphabet set $A$. We use this new
interpretation to give a simple proof of the theorem of Curtis-Hedlund.
