School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, China
Copyright © 2012 Xin Zhang. 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.
Characterizations of strongly compact spaces are given based on the existence of a star-countable open refinement for every increasing open cover. It is proved
that a countably paracompact normal space (a perfectly normal space or a monotonically normal space) is strongly paracompact if and only if every increasing open cover of the space has a star-countable open refinement. Moreover, it is shown that a space is linearly provided that every increasing open cover of the space has a point-countable open refinement.