Hector Alonzo Barriga-Acosta

$\mathfrak{c}$-many types of a $Ψ$-space

We show that for any cardinal $ω<κ\leq \mathfrak{c}$ with $cf(κ) > ω$, there are $\mathfrak{c}$ many AD families whose $Ψ$-spaces are pairwise non-homeomorphic and they can be Luzin families or branch families of $2^ω$.