International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 54689, 13 pages
Sobriety and Localic Compactness in Categories of -Bitopological Spaces
1Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
2Department of Mathematics, Faculty of Science, Assiut University, Assiut 71515, Egypt
Received 9 March 2007; Accepted 24 August 2007
Academic Editor: Francois Goichot
Copyright © 2007 Kamal El-Saady and M. Y. Bakier. 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 notions of -sobriety and -spatiality are introduced for the category -BiTop of -bitopological spaces. Such notions are used to extend the known adjunction
between the category -Top of -topological spaces and the category Loc of locals to one between the category -BiTop and BiLoc. Also, the concepts of localic regularity and localic compactness are introduced in the mentioned category.