reference request - 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.