Products of (weakly) discretely generated spaces

A space X is discretely generated at a point x ∈ X if for any A ⊆ X with x ∈ cl ( A ) , there exists a discrete set D ⊆ A such that x ∈ cl ( D ) . The space X is discretely generated if it is discretely generated at every point x ∈ X . We say that X is weakly discretely generated if for any non-closed set A ⊆ X , there exists a discrete set D ⊆ A such that cl ( D ) ∖ A ≠ ∅ . We obtain new results concerning products of spaces belonging to these classes.