Galois connections between categories of L-topological spaces

A Galois connection between two concrete categories A and B is a pair of concrete functors F:A⟶B,G:B⟶A such that {idY:FG(Y)⟶Y|Y∈B} is a natural transformation from the functor F∘G to the identity functor on B and {idX:X⟶GF(X)|X∈A} is a natural transformation from the identity functor on A to G∘F. In this paper, it is demonstrated that for any complete lattices L1,L2, every Galois connection between the category L1-Top of L1-topological spaces and the category L2-Top of L2-topologically spaces is determined by an L1-topology Δ on L2. Several examples of such Galois connections are given. Under a mild assumption, it is showed that every element of the L1-topology Δ is order-preserving.