All Questions

Let us define the Parovichenko cardinal $\mathfrak{P}$ as the largest cardinal $\kappa$ such that each compact Hausdorff space $K$ of weight $w(K)<\kappa$ is the continuous image of the remainder $...

Since there are L-spaces (provably in ZFC), under CH we have regular, hereditarily Lindelöf spaces with density continuum. However, I cannot find an example of such a space under not CH, nor a proof ...