Illuminability of a subset of the boundary of a convex body (Q801537)

The authors give a sufficient condition for a subset of the boundary of a convex body in \(R^ n\) to be illuminated by a given number of \(k\) directions, \(1\leq k\leq n+d.\) They prove two theorems. Theorem 2: Let \(A=\bar A\subset bd\;V,\) where \(V\) is a bounded convex body in \(R^ n\) and suppose that each n-point subset of \(A\) is illuminated by a single direction. Then the whole of the set A is illuminated by two directions.