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D. De, N. Hindman, and D. Strauss have introduced $C$-set in \cite{key-5},satisfying the strong central set theorem. Using the algebraic structure of theStone-\v{C}ech compactification of a discrete semigroup, N. Hindman and D.Strauss proved that the product of two $C$-sets is a $C$-set. In \cite{key-7},S. Goswami has proved the same result using the elementary characterization of$C$-set. In this paper we prove that the product of two $C$-sets is a $C$-set,using the dynamical characterization of $C$-set.

Note on cartesian product of some combinatorially rich sets