  Suppose S is a planar set. Two points a,b in S 'see each other' via S if
[a,b] is included in S . F. Valentine proved in 1957 that if S is closed, and
if for every three points of S, at least two see each other via S, then S is a
union of three convex sets. The pentagonal star shows that the number three is
best possible. We discard the condition that S is closed and show that S is a
union of (at most) six convex sets. The number six is best possible.
