Covering by discrete and closed discrete sets

Say that a cardinal number κ is small relative to the space X if κ < Δ ( X ) , where Δ ( X ) is the least cardinality of a non-empty open set in X. We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire σ-space and a consistent example of a normal Baire Moore space which can be covered by a small number of discrete sets. We finish with some remarks on linearly ordered spaces.