  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 discuss the following basic question which seems to
be open: Let $K$ and $L$ be infinite compact spaces. Can it happen that
$C_w(K)$ and $C_p(L)$ are homeomorphic?
  M. Krupski proved that the above problem has a negative answer when $K=L$ and
$K$ is finite-dimensional and metrizable. We extend this result to the class of
finite-dimensional Valdivia compact spaces $K$.
