Finite Unions of D-Spaces and Applications of Nearly Good Relation - Xin Zhang; Hongfeng Guo; Yuming Xu (Discrete Dynamics in Nature and Society)
Some results are obtained on finite unions of D-spaces. It is proved that if a space is the union of finitely many locally compact D-subspaces, then it is a D-space. It follows that a space is a D-space if it is the union of finitely many locally compact submetacompact subspaces. And a space is a D-space if it is the union of a D-subspace with a locally compact D-subspace. This partially answers one problem raised by Arhangel’skii. At last, some examples are given to exhibit the applications of nearly good relation to discover D-classes.