2 added 5 characters in body

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.

1

# 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.