On continuous polynomials of the Macías space

Let $\mathbb{N}$ be the set of natural numbers. The Macías space $M(\mathbb{N})$ is the topological space $(\mathbb{N},{\tau }_M)$ where ${\tau }_M$ is generated by the collection of sets ${\sigma }_n:=\{m\in \mathbb{N}:\gcd (n,m)=1\}$. In this paper, we characterize the continuity of polynomials over $M(\mathbb{N})$ and prove that the only continuous polynomials are monomials