embedding a T1 space into a product topology is the following statement true or false:
Let $X$ be a $T_1$ topological space, there exists a cofinite topological space $Y$, such that $X$ can be embedded into ${Y}^J$

This is true by this paper (downloadable) where for a $T_1$ space a cardinal called the Fréchet character $\operatorname{frch}(X)$ is defined. A space $X$ has $\operatorname{frch}(X) \le \omega_\mu$ iff $X$ embeds into a power of spaces $F_\mu$, where this space is the set of ordinals $\le \omega_{\mu}$ in the cofinite topology. 
So we cannot find a single cofinite space that works, but one for every subclass of spaces with some bound on a cardinal. This in contrast to completely regular $T_1$ spaces, that all embed into powers of $[0,1]$ (a so-called generating space).
