Convex sets of almost-normal structure (Q2266411)

A closed and convex subset \(\Omega\) of a Banach space is called a set of almost normal structure if for every closed and convex subset \(K\subset \Omega\) with diam K\(>0\) (the last condition is erroneously omitted in the paper) there exists \(y\in K\) such that \(\| y-k\| <diam K\) for every \(x\in K\). The author constructs a Banach space isomorphic to a Hilbert space with a subset not possessing the almost normal structure.