Points of local nonconvexity, clear visibility, and starshaped sets in Rd

Abstract

Let S be a compact, connected, locally starshaped set in Rd, S not convex. For every point of local nonconvexity q of S, define Aq to be the subset of S from which q is clearly visible via S. Then ker S = ∩{conv Aq: q ∈ lnc S}. Furthermore, if every d+1 points of local nonconvexity of S are clearly visible from a common d-dimensional subset of S, then dim ker S = d.