International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 54689, 13 pages
doi:10.1155/2007/54689
Sobriety and Localic Compactness in Categories of L-Bitopological Spaces
Kamal El-Saady1
and M.Y. Bakier2
1Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
2Department of Mathematics, Faculty of Science, Assiut University, Assiut 71515, Egypt
Abstract
The notions of L-sobriety and L-spatiality are introduced for the category L-BiTop of L-bitopological spaces. Such notions are used to extend the known adjunction between the category L-Top of L-topological spaces and the category Loc of locals to one between the category L-BiTop and BiLoc. Also, the concepts of localic regularity and localic compactness are introduced in the mentioned category.