**
H. Fast**

##
On Intersections of Small Perfect Sets

**abstract:**

For a not empty perfect subset of the unit circle C there is a perfect
subset of C of measure zero which being rotated to every position intersects the
first set on a nonempty perfect set. This result may be stated in terms of a set
of distances between pairs of points from these two sets.

A generalization of this result to a product of tori is suggested.