Covering properties (Q2874873)

This survey covers a wide range of topics, with the three central section titles being: Higher Separation Axioms and Paracompactness; D-Spaces, Linearly Lindelöf and Other Covering Properties; Covering Properties of Products. While many problems, both solved and unsolved, are considered, the authors draw particular attention to the following problems. If every directed open cover of a space \(X\) has a cushioned (\(\sigma\)-cushioned) refinement, is then \(X\) metacompact (submetacompact)? If \(X\) is regular and \(X^\omega\) is hereditarily Lindelöf, is then \(X\) a D-space? Is every Lindelöf space dually discrete? Is every normal, linearly Lindelöf space Lindelöf? Is every 1-star compact Moore space compact? Let \(X\) be a Tychonoff space with \(\kappa = L(X\)). If \(X\times\beta X\) or \(X\times 2^\kappa\) is subnormal, is then \(X\) subparacompact? Is every paracompact product rectangular? Is there a non-normal \(\Sigma\)-product of Lašnev spaces in ZFC? If \(X\) and \(Y\) are paracompact \(\Sigma^\#\)-spaces, is \(X\times Y\) paracompact? Can normality of a \(\Sigma\)-product depend on the choice of the base point?NEWLINENEWLINEFor the entire collection see [Zbl 1282.54001].