Sobriety and Localic Compactness in Categories of L

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

Topological representation and quantic separation axioms of semi-quantales

An adjunction between the category of semi-quantales and the category of lattice-valued quasi-topological spaces is established. Some characterizations of quantic separation axioms, for semi-quantales and lattice-valued quasi-topological spaces, are obtained and some relations among these axioms are established

Net-convergence and weak separation axioms in (L,M)-fuzzy topological molecular lattices

In this paper, we used the concept of (L,M)-fuzzy remote neighborhood system to study and establish the convergence theory of molecular nets. Next, we introduce the Ti-axioms (i = −1,0,1,2) in (L,M)-fuzzy topological molecular lattices, and discuss some of their characterizations. Finally, we show that the Ti-axioms (i = −1,0,1,2) are preserved under homeomorphisms

The category of double fuzzy preproximity spaces

AbstractIn this paper, we introduce the notions of double neighborhood systems and double fuzzy preproximity in double fuzzy topological spaces. We used double neighborhoods to study the initial structure of double fuzzy topological spaces, and the joins between them and the initial structures of double fuzzy preproximity spaces. Furthermore, we have proved that the category of double fuzzy preproximity spaces is a topological category, and hence a topological construct