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.



Do separable and normal have topological meanings for fields?
This is incorrect. Words like "separable" and "normal" occur in unrelated ways in various parts of mathematics. (Normal subgroup, separable differential equations...)
Other words, too. Like "regular", "perfect" ...


"Separable" in toplogy... Does it mean something can be "separated"? What? I believe it goes back to Fréchet, but what did he mean by it?


