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 id : FG(Y) -> Y vertical bar Y is an element of B} is a natural trtransformationrom the functor F circle G to the identity functor on B and {idx : X -> GF(X) vertical bar X is an element of A} is a natural transformation from the identity functor on A to G circle F. In this paper, it is demonstrated that for any complete lattices L(1), L(2), every Galois connection between the category L(1) -Top of L(1) -topological spaces and the category L(2)-Top of L(2)-topologically spaces is determined by an L(1)-topology Delta on L(2). Several examples of such Galois connections are given. Under a mild assumption, it is showed that every element of the L(1)-topology Delta is order-preserving. (c) 2004 Elsevier B.V. All rights reserved.
galois connection l-topological space complete lattice topological category