pi-base
Novak space definition is wrong
The current definition of Novak space is wrong and needs to be fixed. Indeed, if we were to take $P_A = \emptyset$ for all $A$ then we would obtain $\mathbb{N}$.
The definition of the family $P_A$ is supposed to be contained in point 1 of #112 in Counterexamples, but that's wrong too!
The only resource we can possibly use is the original article by Novak.
https://eudml.org/doc/213312
Note that Novak uses some weird nomenclature, for example by "compact" he actually means countably compact.
This points out another problem of pi-base, a lot of spaces from Counterexamples were defined in a way that's been very neglectful, and not a lot of them have been supervised and understood before having been added to pi-base. For example, all the screw constructions.
I haven't explained the exact reason why Counterexamples is wrong, but the reason is basically that in their argument they use that the cardinal they are working with is a regular cardinal, which is not necessarily true. You need to apply the argument of Novak.