  We give an example of an infinite metrizable space $X$ such that the space
$C_p(X)$, of continuous real-valued function on $X$ endowed with the pointwise
topology, is not homeomorphic to its own square $C_p(X)\times C_p(X)$. The
space $X$ is a zero-dimensional subspace of the real line. Our result answers a
long-standing open question in the theory of function spaces posed by A.V.
Arhangel'skii.
