My question arises from a step in the proof of Theorem 3 in Katětov's paper. In it, he states (where $P:=\prod\limits_{n=1}^\infty P_n$ is a completely normal space) -
We may suppose $P$ infinite, so that it contains (the discontinuum of Cantor, and, therfore) a countable non-closed set.
How did Katětov come about this? I'm assuming by 'the discontinuum of Cantor', he means what we call now the Cantor set. So, where did the Cantor set come from? Any help will be appreciated!
The Cantor set is homeomorphic to $\{0,1\}^{\Bbb N}$ (discrete $\{0,1\}$) and this surely embeds into $P$ (we only need infinitely many $P_n$ with at least two points, and a two point set is homeomorphic to $\{0,1\}$ etc.)