Recall that $X$ is in the class dual to the spaces with the Souslin property: For any neighbourhood assignment $\{O_x: x\in X\}$, there is a subspace $Y \subseteq X$ such that $c(Y)=\omega$ and $\bigcup \{O_x: x\in Y\}=X.$
Let $X=\{\xi: \xi \in \mathfrak {c}^+; cf(\xi)=\omega\}$. Is the space $X$ in the class dual to the spaces with the Souslin property?
Thanks for your help.