## Do separable and normal have topological meanings for fields?

The terminology would suggest that a separable field extension is so because the resulting field extension has some sort of separable topology, and that a normal extension corresponds to one with a normal topology.

I imagine this is true, or else they wouldn't have named them in such a way.

Also, I'm not sure what subfield this falls under, so if you could suggest additional tags, that would be great as well.

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 Separable has a topological meaning that is not T_2. See also: mathoverflow.net/questions/7389/… – Jonas Meyer Feb 22 2010 at 2:02 I see your edit has made part of my comment irrelevant, but the link is intended to get across the same point as Gerald Edgar's answer. – Jonas Meyer Feb 22 2010 at 2:36 Then I misunderstood your comment. After reading it I thought there still was some connection, and mining the link for information came back with nothing, so I was still in a state of confusion. Simply saying "This is incorrect." answers my question better. – Andrew Homan Feb 22 2010 at 2:53 The "normal" in "normal extension" comes from normal subgroups, or maybe the other way around. The "separable" in "separable extension" comes from separable polynomials, i.e. polynomials whose roots are distinct (hence can be "separated"). – Qiaochu Yuan Feb 22 2010 at 3:53