  A frequently repeated claim in the "applied Koopman operator theory''
literature is that a dynamical system with multiple isolated equilibria cannot
be linearized in the sense of admitting a smooth embedding as an invariant
submanifold of a linear dynamical system. This claim is sometimes made only for
the class of super-linearizations, which additionally require that the
embedding "contain the state''. We show that both versions of this claim are
false by constructing (super-)linearizable smooth dynamical systems on
$\mathbb{R}^k$ having any countable (finite) number of isolated equilibria for
each $k>1$.
