This is an announcement for the paper "On isomorphisms of Banach spaces of continuous functions" by Grzegorz Plebanek. Abstract: We prove that if $K$ and $L$ are compact spaces and $C(K)$ and $C(L)$ are isomorphic as Banach spaces then $K$ has a $\pi$-base consisting of open sets $U$ such that $\overline{U}$ is a continuous image of some compact subspace of $L$. This gives some information on isomorphic classes of the spaces of the form $C([0,1]^\kappa)$ and $C(K)$ where $K$ is Corson compact. Archive classification: math.FA Mathematics Subject Classification: Primary 46B26, 46B03, 46E15 Remarks: 15 pages Submitted from: grzes@math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.3211 or http://arXiv.org/abs/1302.3211