  For a compact space $K$ we denote by $C_w(K)$ ($C_p(K)$) the space of
continuous real-valued functions on $K$ endowed with the weak (pointwise)
topology. In this paper we address the following basic question which seems to
be open: Suppose that $K$ is an infinite (metrizable) compact space. Is it true
that $C_w(K)$ and $C_p(K)$ are homeomorphic? We show that the answer is "no",
provided $K$ is an infinite compact metrizable $C$-space. In particular our
proof works for any infinite compact metrizable finite-dimemsional space $K$.
