D-spaces: (1) Extent and Lindelöf numbers

This is the first of a series of talks based on Gary 
Gruenhage's 'A survey of D-spaces' [1]. A space is D if for every 
neighbourhood assignment we can choose a closed discrete set of points 
whose assigned neighbourhoods cover the space. The mention of 
neighbourhood assignments and a topological notion of smallness (that 
is, of being closed and discrete) is peculiar among covering properties. 
Despite being introduced in the 70's, we still don't know whether a 
Lindelöf or a paracompact space must be D. In this talk, we will examine 
some elementary properties of this class via extent and Lindelöf numbers.