Weak calibers and the Scott-Watson theorem
Weak covering properties and the class MOBI
Weakly closed multifunctions and paracompactness.
Weakly compactly generated Frechet spaces.
When is Lindelöf?
Theorem. In ZF (i.e., Zermelo-Fraenkel set theory without the axiom of choice) the following conditions are equivalent: (1) is a Lindelöf space, (2) is a Lindelöf space, (3) is a Lindelöf space, (4) every topological space with a countable base is a Lindelöf space, (5) every subspace of is separable, (6) in , a point is in the closure of a set iff there exists a sequence in that converges to , (7) a function is continuous at a point iff is sequentially continuous at , (8)...
Which topological spaces have a weak reflection in compact spaces?
The problem, whether every topological space has a weak compact reflection, was answered by M. Hušek in the negative. Assuming normality, M. Hušek fully characterized the spaces having a weak reflection in compact spaces as the spaces with the finite Wallman remainder. In this paper we prove that the assumption of normality may be omitted. On the other hand, we show that some covering properties kill the weak reflectivity of a noncompact topological space in compact spaces.