On Sets Which Meet Each Line in Exactly Two Points

  title={On Sets Which Meet Each Line in Exactly Two Points},
  • Published 1997
Using techniques from geometric measure theory and descriptive set theory, we prove a general result concerning sets in the plane which meet each straight line in exactly two points. As an application we show that no such "two point" set can be expressed as the union of countably many rectiiable sets together with a set with Hausdorr 1-measure zero. Also, as another corollary, we show that no analytic set can be a two point set provided every purely unrectiiable set meets some line in at least… CONTINUE READING