Constructing crowded Hausdorff $P$-spaces in set theory without the axiom of choice

Eleftherios Tachtsis, Eliza Wajch

For an infinite set $X$, a closed under finite unions family $\mathcal{Z}$ with $[X{]}^{<\omega }\subseteq \mathcal{Z}\subseteq \mathcal{P}(X)$, and any $\mathcal{A}\subseteq \mathcal{P}(X)$,…