On the illumination of unbounded closed convex sets (Q1802776)

A closed convex set \(K\subset R^ d\) is called almost bounded if there is a \(d\)-dimensional ball that intersects every supporting hyperplane of \(K\). Let \(L\) denote the orthogonal complementary subspace of the affine hull of the recession cone of \(K\). It is proved here that the minimum number of \(k\)-dimensional subspaces needed to illuminate the \(d\)- dimensional almost bounded convex set \(K\) is not larger than the minimum number of \(k\)-dimensional subspaces of \(L\) needed to illuminate the closure of the projection of \(K\) onto \(L\).