  Let $R$ be a commutative ring and $M$ an $R$-module. Let $Spec^s(M)$ be the
the collection of all second submodules of $M$. In this article, we consider a
new topology on $Spec^s(M)$, called the second classical Zariski topology, and
investigate the interplay between the module theoretic properties of $M$ and
the topological properties of $Spec^s(M)$. Moreover, we study $Spec^s(M)$ from
point of view of spectral space.
