Topological rigidity of closures of certain sparse unipotent orbits in finite-volume quotients of ${\prod }_{i=1}^k{\mathrm{SL}}_2(\mathbb{R})$

We give a simple proof about the topological rigidity of closures of certain sparse unipotent orbits in $G\mathrm{/}\mathrm{\Gamma }$ where $G={\prod }_{i=1}^k{\mathrm{SL}}_2(\mathbb{R})$ and $\mathrm{\Gamma }$ is an irreducible lattice in $G$.