If a set $S$ is endowed with the discrete topology $\mathcal{P}(S)$, then for every normal space $N$ the product $S\times N$ is normal.


**Question**: can we endow a set $S$ with another Hausdorff topology, such that still for all normal spaces $N$ the product $S\times N$ is normal.



"Productively normal" space
The answer is no. It was proved by Mary Ellen Rudin in *$\aleph$-Dowker spaces* (1978) that for any non-discrete Hausdorff space $S$ there is a normal Hausdorff space $N$ such that $S\times N$ is not normal, thus solving in the affirmative [Morita´s first conjecture](http://en.wikipedia.org/wiki/Morita_conjectures).


