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Let K/F be an infinite Galois extension, and let N be a normal sub-group of Gal(K/F). Show that N closure is a normal subgroup of Gal(K/F).

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    the closure of a normal subgroup in any topological group is normal2012-10-31
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    I have this proof. But can we do it w/o topological group?2012-10-31
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    Without topology, what do you mean by closure?2012-11-02
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    I am seeking a proof using Fundamental Theorem of Infinite Galois Theory. Possibly by showing Fixed field of N closure is Galois over F.2012-11-02
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    Okay!! I have got it. Thanks, anyway!2012-11-06

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