The natural topology on $\mathbb{R}$ was used to defined ultrafilter near
zero by N. Hindman and I. Leader. They showed that a small part closed to zero
like the discrete case has rich combinatorial properties. In the weakly almost
periodic compactification of discrete topological semigroup $S$, is denoted by
$S^w$, idempotents can act like zero in $(0,+\infty)$. In fact, for an
idempotent $e\in S^w$ the collection of all ultrafilters near $e$ is defined
and form a compact subsemigroup of $\beta S_d$, where $S_d$ is $S$ with
discrete topology. In this paper, we will show that Central set Theorem holds
near an idempotent of the weakly almost periodic compactification from a
discrete semigroup. Also some facts near zero will be state near an idempotent.