In this work, we examine the topology of special type of sequences in which each candidate is a polynomial with its coefficients are of integers taken from a discrete set. The paper develops a different perspective with regard to the recent progress in the theory of polynomials with bounded integer coefficients. In the context of discrete control systems, we apply the theory to one dimensional reachability problem of a convex polyhedra with finite number of controls acting on the system and prove that the reachable set of the discrete model is dense in the set of real numbers under the suitable finite control set