The D-property of monotone covering properties and related conclusions
In this note, it is shown that every monotonically (countably) metacompact space is hereditarily a \(D\)-space and every monotonically meta-Lindelöf space is hereditarily dually \(\sigma\)-closed discrete. As a corollary, it is shown that if \(X\) is a monotonically meta-Lindelöf (or monotonically (countably) metacompact) monotonically normal space then \(X\) is hereditarily paracompact. In the second part of this note, the authors show that every scattered partition of a hereditarily almost thickly covered space is almost thick, and hence a hereditarily almost thickly covered space is \(aD\) and linearly \(D\). This answers a question of Guo and Junnila. It is also shown that every monotonically \(\omega\)-monolithic compact space is monotonically monolithic. This answers a question of Alas, Tkachuk and Wilson.
scientific article; zbMATH DE number 6084114
scientific article