DISCRETE SETS AND THE CARDINALITY OF A LINEARLY LINDELOF SPACE

The depth g(X) of a space X is the supremum of the cardinalities of closures of discrete sets of X. Recently, Spadaro proved a cardinality bound for a Hausdorff space X involving g(X) and the Lindelof degree L(X). We try to extend this result by replacing the Lindelof degree with the linear Lindelof degree. We will do it for Tychonoff spaces and consistently in the general case.