Almost ball remotal subspaces in Banach spaces (Q2919695)

The author continues his study of the set of remotal (farthest) points in a Banach space \(X\), by considering the notion of almost ball remotal subspaces \(Y \subset X\). This happens when the set of farthest points in \(X\) to the unit ball of \(Y\) contains a dense \(G_{\delta}\)-set. It is shown that in the space of continuous functions on a compact set, any closed ideal has this property. Under some additional conditions, this notion is also preserved by direct sums.