arXiv subjects
Publications and source records attributed to César Corral.
We give examples of $n$-sequentially compact spaces that are not $(n+1)$-sequentially compact under several assumptions. We improve results from Kubis and Szeptycki by building such examples from $\mathfrak{b=c}$ and $\diamondsuit(\mathfrak{b})+\mathfrak{d}=ω_1$. We also introduce a new splitting-like cardinal invariant and then show that the same holds under $\mathfrak{s=b}$.
We give a combinatorial characterization of countable submaximal subspaces of $2^κ$. Using a parametrized version of Mathias forcing, we prove that there exists a countable submaximal subspace of $2^{ω_1}$ whilst $\mathfrak{c}=ω_2$. Combining this with previous results, we construct a disjointly tight countable irresolvable space of weight $<\mathfrak{c}$, answering a question of Bella and Hrušák.
We consider weakenings of normality in $Ψ$-spaces and prove that the existence of a MAD family whose $Ψ$-space is almost-normal is independent of \textsf{ZFC}. We also construct a partly-normal not quasi-normal AD family, answering questions from García-Balan and Szeptycki. We finish by showing that the concepts of almost-normal and strongly $\aleph_0$-separated AD families are different, even under \textsf{CH}, answering a question from Oliveira-Rodrigues and Santos-Ronchim