Let $R$ be a commutative ring with $1$ and $I$ be an ideal of $R$. Now let $J=\cap_{I\subseteq m\in Max(R)}m$. Set $A:=\{p\in Spec(R): I\subseteq p\}$ and $B:=\{p\in Spec(R): J\subseteq p\}$, where $Spec(R)$ and $Max(R)$ are the set of all prime and maximal ideals of $R$ respectively. When considering $Spec(R)$ with the Zariski topology, and $B$ and $A$ as two subspaces of $Spec(R)$.I want if $B$ is dense in $A$? Or in general, what kinds of topological properties hold between $A$ and $B$?