On the Lindelöf property
by
Gareth Davies
Mathematical Institute, Oxford University

On the surface, Lindelöfness seems as easy to work with as compactness. However, while there are many characterisations of compactness, it is not clear that the analogous formulations of Lindelöfness are equivalent. We consider one such formulation, that of being dually Lindelöf with respect to neighbourhood assignments. A space X is said to have this property if for every neighbourhood assignment {O_x | x ∈ X}, there is a Lindelöf subspace Y of X, such that {O_y | y ∈ Y} covers X. Among other things, we will see that this property is strictly weaker than Lindelöfness (a result by O. T. Alas, V. V. Tkachuk, and R. G. Wilson).

Date received: May 23, 2008