International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1869-1878
Semicompactness in -topological spaces
Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China
Received 8 October 2004; Revised 8 June 2005
Copyright © 2005 Fu-Gui Shi. 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.
The concepts of semicompactness, countable semicompactness, and
the semi-Lindelöf property are introduced in -topological
spaces, where is a complete de Morgan algebra. They are
defined by means of semiopen -sets and their inequalities. They
do not rely on the structure of basis lattice and no distributivity in is required. They can also be characterized by semiclosed -sets
and their inequalities. When is a completely distributive de
Morgan algebra, their many characterizations are presented.