D-spaces and thick covers

The following results are obtained.– n neighbornet U of X has a closed discrete kernel if X has an almost thick cover by countably U-close sets. hereditarily thickly covered space is aD and linearly D. t-metrizable space is a D-space. D-space if X has a cover { X α : α < λ } by D-subspaces such that, for each β < λ , the set ⋃ { X α : α < β } is closed.