Bourbaki

Exercise 14, § 2

Topological Vector Spaces, I, p. 28

Generalize the results of Nos. 2 and 3 to topological vector spaces E over a discrete field K, such that there exists a fundamental system of balanced neighborhoods of 0 in E (i.e. of neighborhoods V such that K.V = V).

Solution

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Machine translation of the English, by gpt-5-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.