On subspaces of pseudoradial spaces

Abstract:

A topological space $X$ is pseudoradial if each of its non closed subsets $A$ has a sequence (not necessarily with countable length) convergent to outside of $A$. We prove the following results concerning pseudoradial spaces and the spaces $\omega \cup \{p\}$, where $p$ is an ultrafilter on $\omega$: (i) CH implies that, for every ultrafilter $p$ on $\omega$, $\omega \cup \{p\}$ is a subspace of some regular pseudoradial space. (ii) There is a model in which, for each P-point $p$, $\omega \cup \{p\}$ cannot be embedded in a regular pseudoradial space while there is a point $q$ such that $\omega \cup \{q\}$ is a subspace of a zero-dimensional Hausdorff pseudoradial space.