Let formula_70 be a Galois extension (possible infinite) and let formula_71 be the Galois group of the extension. Let formula_72be the set of the Galois groups of all finite intermediate Galois extension. Note that for all formula_73 we can define the maps formula_74 by formula_75. We then define the "Krull Topology" on formula_54 to be weakest topology such that for all formula_73 the maps formula_74 are continuous, where we endow each formula_79 with the discrete topology. Stated differently formula_80 as an inverse limit of topological groups (where again each formula_79 is endowed with the discrete topology). This makes formula_54 a profinite group (in fact every profinite group can be realised as the Galois group of a Galois extension, see for example ). Note that when formula_60 is finite, the Krull topology is the discrete topology.