Cardinal inequalities involving the Hausdorff pseudocharacter

We establish several bounds on the cardinality of a topological space involving the Hausdorff pseudocharacter H psi (X). This invariant has the property psi(c)(X) <= H psi( X) <= chi(X) for a Hausdorff space X. We show the cardinality of a Hausdorff space X is bounded by 2(pwLc(X) H psi(X)), where pwL(c)( X) <= L(X) and pwL(c)( X) <= c( X). This generalizes results of Bella and Spadaro, as well as Hodel. We show additionally that if X is a Hausdorff linearly Lindelof space such that H psi( X) = omega, then vertical bar X vertical bar <= 2(omega), under the assumption that either 2(