Sobriety and Localic Compactness in Categories ofL-Bitopological Spaces

Abstract

The notions ofL-sobriety andL-spatiality are introduced for the categoryL-BiTop ofL-bitopological spaces. Such notions are used to extend the known adjunction between the categoryL-Top ofL-topological spaces and the category Loc of locals to one between the categoryL-BiTop and BiLoc. Also, the concepts of localic regularity and localic compactness are introduced in the mentioned category.