This paper gives over 15 results relating nearly a dozen subtly defined properties. For readability, this review mentions only a few of these results relating only a few of these properties. The results mentioned in this review all end in “then is a -space,” but many of the results in this paper do not have this format.
Recall that is a -space iff, given an open cover where each , there is a closed discrete so that .
To give the flavor of this paper, here are three results:
If has an almost thick cover by closed Lindelöf -sets, then is a -space.
Here a cover is almost thick iff there is a finite union of elements of so that if and is not closed then there is with cl.
If is -metrizable, then is a -space.
Here a space is -metrizable iff it has a finer metrizable topology and a function so that if then cl cl.
If is a union of finitely many screenable -spaces, then is a -space.
Here a -space is one with a -discrete closed network; a space is screenable iff each open cover has a -pairwise disjoint open refinement.