4 problems

A topological space $X$ is a perfectly normal wQN-space if it is perfectly normal and has the wQN property; equivalently in this context, it is an $s_1$-space, meaning that…

Productive weak-property conjectures. If a space is productively Menger then it is productively weakly Menger. If a space is productively Hurewicz then it is productively weakly Hu…

Let $X$ be a metrizable space. The Menger–screenability conjecture asserts that there is such an $X$ with the Menger property and … which does not have the Haver property in some m…

Product selection-principle theorem. If $Y$ has ${\sf S}_c(\mathcal{O},\mathcal{O})$ and ${\sf S}_{fin}(\Omega,\mathcal{O}^{gp})$, then $X\times Y$ has…