International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1869-1878
doi:10.1155/IJMMS.2005.1869
Semicompactness in L-topological spaces
Fu-Gui Shi
Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China
Abstract
The concepts of semicompactness, countable semicompactness, and the semi-Lindelöf property are introduced in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of semiopen L-sets and their inequalities. They do not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by semiclosed L-sets and their inequalities. When L is a completely distributive de Morgan algebra, their many characterizations are presented.