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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 12, Pages 1869-1878
http://dx.doi.org/10.1155/IJMMS.2005.1869

Semicompactness in L-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 Hindawi Publishing Corporation. 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

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.