Copyright © 2013 Xin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Some results are obtained on finite unions of -spaces. It is proved
that if a space is the union of finitely many locally compact -subspaces, then it
is a -space. It follows that a space is a -space if it is the union of finitely many
locally compact submetacompact subspaces. And a space is a -space if it is the
union of a -subspace with a locally compact -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 -classes.