Let formula_84 denote the set of all finite intermediate field extension of formula_60 and let formula_86 denote the set of all closed subgroups of formula_71 endowed with the Krull topology. Then there exists a bijection between formula_84 and formula_86 given by the mapformula_90defined by formula_91 and the map formula_92defined by formula_93. One important thing one need to check is that formula_94 is a well-defined map, that is that formula_95 is a closed subgroup of formula_54 for all intermediate. For a proof see for example