This is an announcement for the paper “Relatively weakly open convex combinations of slices” by Trond A. Abrahamsen<https://arxiv.org/find/math/1/au:+Abrahamsen_T/0/1/0/all/0/1>, Vegard Lima<https://arxiv.org/find/math/1/au:+Lima_V/0/1/0/all/0/1>. Abstract: We show that $c_0$, and in fact $C(K)$ for any scattered compact Hausdorff space $K$, have the property that finite convex combinations of slices of the unit ball are relatively weakly open. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.06169