Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10324344 | Fuzzy Sets and Systems | 2005 | 10 Pages |
Abstract
A Galois connection between two concrete categories A and B is a pair of concrete functors F:Aâ¶B,G:Bâ¶A such that {idY:FG(Y)â¶Y|YâB} is a natural transformation from the functor FâG to the identity functor on B and {idX:Xâ¶GF(X)|XâA} is a natural transformation from the identity functor on A to GâF. 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 Î on L2. Several examples of such Galois connections are given. Under a mild assumption, it is showed that every element of the L1-topology Î is order-preserving.
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Authors
Dexue Zhang,