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.