On spaces which are linearly D

We introduce a generalization of D-spaces, which we call linearly D-spaces. The following results are obtained for a T1-space X.–X is linearly Lindelöf if, and only if, X is a linearly D-space of countable extent.–X is linearly D provided that X is submetaLindelöf.–X is linearly D provided that X is the union of finitely many linearly D-subspaces.–X is compact provided that X is countably compact and X is the union of countably many linearly D-subspaces.