@Mueller: I'm beginning to suspect that Delgado is wrong in his claim, particularly the 'immediacy' of the deduction...

@Brandenburg: ditto.

@Quid: Yes, this is what I was getting at.

@Tveiten: I have, and I still don't think its answered my question. They go via the route of characterising Galois extensions first as algebraic, separable & normal extensions - and then show the property that Delgado uses to characterise a Galois extension follows. Whereas Delgado starts of with this and deduces the characterisation.

By denying that it's answerable in its own terms? When Newton wrote about his law of gravitation, he made certain he could model both time and space mathematically, the background to his physics. I'm denying that this background is available in economics. Theories don't exist in a vacuum , they exist in a larger theoretical space.

I don't think Vitale deserved the brushoff that the moderators have given him. I certainly think the arithmatic derivative is an intriguing idea, and Vitale should have been encouraged to phrase his question in a more sensible fashion: such as has there been any interesting results shown/proved/reformulated.

and your additional comment is useful too.

great, going by Lees answer I see that my question wasn't quite right. But I am interested in how I phrased it. Do you think it can actually hold locally? I've accepted Lees answer as it only seems fair since I picked up the question from his book. But your answer is equally worthwhile. It doesn't seem quite correct that one should choose.

I wasn't expecting the author of the text to turn up! Thanks, what you had in mind wasn't what I was expecting, but I see now I should have done, its exactly analogous to final maps in Top.