  We prove that for every infinite set $E\subset \mathbb Z$, there is a set
$S\subset E-E$ which is a set of topological recurrence and not a set of
measurable recurrence. This extends a result of Igor Kriz, proving that there
is a set of topological recurrence which is not a set of measurable recurrence.
Our construction follows Kriz's closely, and this paper can be considered an
exposition of the original argument.
