Extensions of L-fuzzy closure spaces

In this paper, we study the extension theory to L-fuzzy closure spaces, where L is a strictly two-sided, commutative quantale lattice. We give new notions such as L-fuzzy stack, L-fuzzy c-grill and trace of a point. Also, we construct order relation and equivalence relation between two extensions. Also, We introduce the concept of a principal extension of L-fuzzy closure space and study some of its applications.