  Combinatorially Rich sets were introduced by Bergelson and Glasscock for
commutative semigroup. Latter Hindman, Hosseini, Strauss and Tootkaboni
extended the definition of Combinatorially Rich sets for arbitrary semigroup.
Recently Goswami proved that product of two Combinatorially Rich sets is also a
Combinatorially Rich set. On the other hand Hindman and Leader were the first
to introduce the concept of central sets near zero for dense semigroups of
$\left(\left(0,\infty\right),+\right)$ and demonstrated an important
combinatorial consequence regarding these sets. In this article we provided
dynamical and combinatorial characterization of essential CR-sets near zero and
explore the cartesian product of these sets.
