Finite Unions of D-Spaces and Applications of Nearly Good Relation

Abstract EN

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.