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

Abstract

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

6 pages