A Lindelöf space with no Lindelöf subspace of size $\aleph \textunderscore 1$
A Lindelöf space with no Lindelöf subspace of size $\aleph \textunderscore 1$
A consistent example of an uncountable Lindelöf $T_3$ (and hence normal) space with no Lindelöf subspace of size $\aleph _1$ is constructed. It remains unsolved whether extra set-theoretic assumptions are necessary for the existence of such a space. However, our space has size $\aleph _2$ and is a $P$-space, i.e., …