Countability axioms in I-fuzzy topological spaces

In this paper, we introduce the concepts of first countability, second countability, density, separability, and Lindelöf property for I-fuzzy topological spaces, and study their properties and the relationships between them. Furthermore, we give the Lindelöf theorem in I-fuzzy topological spaces and describe fuzzy continuous maps by convergence of sequences. Finally, we discuss the productive property of first countability of I-fuzzy topological spaces.