# Factor Spaces are T4 if Product Space is T4

## Theorem

Let $\mathbb S = \left\{{\left({S_\alpha, \tau_\alpha}\right)}\right\}$ be a set of topological spaces for $\alpha$ in some indexing set $I$.

Let $\displaystyle T = \left({S, \tau}\right) = \prod \left({S_\alpha, \tau_\alpha}\right)$ be the product space of $\mathbb S$.

Let $T$ be a $T_4$ space.

Then each of $\left({S_\alpha, \tau_\alpha}\right)$ is a $T_4$ space.