Staircase convex results for a certain class of orthogonal polytopes (Q2354666)

A starshapeness condition of Krasnosel'skii type is obtained in the framework of finite unions \(S\) of boxes in \(\mathbb{R}^{d}\) whose intersection graph is a connected block graph. The main theorem is stronger than the existing ones in literature, since it places some particular subsets of \(S\) in a staircase convex subset. As consequence, it is shown that when \(S\) is staircase starshaped then \(KerS\) is staircase convex. More results on staircase convex sets and their unions are derived from these results.