Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 808262, 4 pages
http://dx.doi.org/10.1155/2013/808262
Research Article

Finite Unions of -Spaces and Applications of Nearly Good Relation

Xin Zhang,1 Hongfeng Guo,1 and Yuming Xu2

1School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, China
2School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received 14 January 2013; Accepted 7 April 2013

Academic Editor: Fuyi Xu

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.

Abstract

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.