This is an announcement for the paper “On the weak and pointwise topologies in function spaces II” by Mikołaj Krupskihttp://arxiv.org/find/math/1/au:+Krupski_M/0/1/0/all/0/1, Witold Marciszewskihttp://arxiv.org/find/math/1/au:+Marciszewski_W/0/1/0/all/0/1.

Abstract: 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 $K$.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1608.03883