This purpose of this book is to study stratified L-grill structure, supra (L,M)-closure operator, initial (L,M)-closure operator, lattice valued double syntopogenous structures, stratified double L-topological structures and double LC-uniform space; covering approach, where L, M are strictly two sided commutative quantale lattices. We presented notions and several results such as the relationships among them, continuity of mappings, products and some fundamental properties are established.

Dr. Abd-Allah Nassr Elseleny (Assistant Professor), Pure Mathematics (Topology), Faculty of Science,Jazan University, Saudi Arabia