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.
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