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The terminology would suggest that a separable field extension is so because the resulting field extension has some sort of $T_2$ separable topology, and that a normal extension corresponds to one with a $T_4$ 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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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 $T_2$ topology, and that a normal extension corresponds to one with a $T_4$ 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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