Separation axioms in fuzzy bitopological spaces

Abstract

In this paper, lattice-valued analogues of T_i separation axioms for fuzzy bitopological spaces where i ∈ {0, 1, 2, 3, 4} are introduced, employing the notion of neighborhood filter of W. Gähler. In the case of L = {0, 1}, the axioms in question reduce to the classical separation axioms of general topology. Additionally, these lattice-valued generalizations have many properties of their corresponding crisp analogues. Also, showing that these separation axioms are good extensions in the sense of R. Lowen.