Classical intermediate factor theorems establish settings of measure-class preserving maps $G\curvearrowright Y$ and $G\curvearrowright X$ such that every G-intermediate factor Q with $Y\times X\rightarrow Q\rightarrow Y$ splits as a product of Y and a factor of X. In this talk, we present some topological versions of these intermediate factor theorems and also discuss possible generalizations on tensor product splitting in $C^*$-algebras. Based on joint work with Amrutam Tattwamasi.